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324: Paper Source PDF document

Paper's Title:

Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: http://rgmia.org/dragomir 

Abstract:

The main aim of this survey is to present recent results concerning Ostrowski type inequalities for the Lebesgue integral of various classes of complex and real-valued functions. The survey is intended for use by both researchers in various fields of Classical and Modern Analysis and Mathematical Inequalities and their Applications, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.



292: Paper Source PDF document

Paper's Title:

Inequalities for Functions of Selfadjoint Operators on Hilbert Spaces:
a Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, College of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: https://rgmia.org/dragomir 

Abstract:

The main aim of this survey is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.



229: Paper Source PDF document

Paper's Title:

Inequalities for Discrete F-Divergence Measures: A Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: http://rgmia.org/dragomir 

Abstract:

In this paper we survey some recent results obtained by the author in providing various bounds for the celebrated f-divergence measure for various classes of functions f. Several techniques including inequalities of Jensen and Slater types for convex functions are employed. Bounds in terms of Kullback-Leibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the f-divergence measure by the use of the celebrated Ostrowski and Trapezoid inequalities are obtained. More accurate approximation formulae that make use of Taylor's expansion with integral remainder are also surveyed. A comprehensive list of recent papers by several authors related this important concept in information theory is also included as an appendix to the main text.



130: Paper Source PDF document

Paper's Title:

Hermite-Hadamard Type Inequalities for MN-Convex Functions

Author(s):

Sever S. Dragomir1,2

1Mathematics, College of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: https://rgmia.org/dragomir 

Abstract:

The present work endeavours to briefly present some of the fundamental results connected to the Hermite-Hadamard inequality for special classes of convex functions such as AG, AH, GA, GG, GH, HA, HG and HH -convex functions in which the author have been involved during the last five years. For simplicity, we call these classes of functions such as MN-convex functions, where M and N stand for any of the Arithmetic (A), Geometric (G) or Harmonic (H) weighted means of positive real numbers. The survey is intended for use by both researchers in various fields of Approximation Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.



68: Paper Source PDF document

Paper's Title:

Inequalities for the Čebyšev Functional of Two Functions of Selfadjoint Operators in Hilbert Spaces

Author(s):

S. S. Dragomir

School of Engineering and Science
 Victoria University, PO 14428
 Melbourne City MC, Victoria 8001,
Australia

sever.dragomir@vu.edu.au
URL
: http://www.staff.vu.edu.au/RGMIA/dragomir/

Abstract:

Some recent inequalities for the Čebyšev functional of two functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and operators, are surveyed.



20: Paper Source PDF document

Paper's Title:

Some Grüss Type Inequalities in Inner Product Spaces

Author(s):

Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa

URL: http://rgmia.org/dragomir 

Abstract:

Some inequalities in inner product spaces that provide upper bounds for the quantities

and  ,

where e,f ∈ H with and x,y are vectors in H satisfying some appropriate assumptions are given. Applications for discrete and integral inequalities are provided as well.



16: Paper Source PDF document

Paper's Title:

New Reverses of Schwarz, Triangle and Bessel Inequalities in Inner Product Spaces

Author(s):

S. S. Dragomir

School of Computer Science and Mathematics, Victoria University of Technology, PO BOX
14428, MCMC 8001, VICTORIA, AUSTRALIA.

sever.dragomir@vu.edu.au
URL
: http://rgmia.vu.edu.au/SSDragomirWeb.html

Abstract:

New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in the earlier paper [13]. Further, they are employed to establish new Grüss type inequalities. Finally, some natural integral inequalities are stated as well.



16: Paper Source PDF document

Paper's Title:

Some Operator Order Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

Author(s):

S. S. Dragomir1,2 and Charles E. M. Pearce3

1Mathematics, School of Engineering & Science,
Victoria University,
PO Box 14428, Melbourne City, MC 8001,
Australia.

2School of Computational & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.

sever.dragomir@vu.edu.au 
URL: http://rgmia.org/dragomir

3School of Mathematical Sciences,
The University of Adelaide,
Adelaide,
Australia
 

Abstract:

Various bounds in the operator order for the following operator transform

where A is a selfadjoint operator in the Hilbert space H with the spectrum
Sp( A) ⊆ [ m,M] and f:[m,M] ->  C is a continuous function on [m,M]  are given. Applications for the power and logarithmic functions are provided as well.



15: Paper Source PDF document

Paper's Title:

Further Bounds for Two Mappings Related to the Hermite-Hadamard Inequality

Author(s):

S. S. Dragomir1,2 and I. Gomm1

1Mathematics, School of Engineering & Science,
Victoria University,
PO Box 14428, Melbourne City, MC 8001,
Australia.

2School of Computational & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.

sever.dragomir@vu.edu.au
ian.gomm@vu.edu.au
URL: http://rgmia.org/dragomir  
 

Abstract:

Some new results concerning two mappings associated to the celebrated Hermite-Hadamard integral inequality for twice differentiable functions with applications for special means are given.



15: Paper Source PDF document

Paper's Title:

Inequalities for the Area Balance of Functions of Bounded Variation

Author(s):

Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: http://rgmia.org/dragomir 

Abstract:

We introduce the area balance function associated to a Lebesgue integrable function f:[a,b] C by

Several sharp bounds for functions of bounded variation are provided. Applications for Lipschitzian and convex functions are also given.



13: Paper Source PDF document

Paper's Title:

Reverses of the CBS Integral Inequality in Hilbert Spaces and Related Results

Author(s):

I. Brnetić, S. S. Dragomir, R. Hoxha and J. Pečarić

Department of Applied Mathematics, Faculty of Electrical Engineering and Computing,
University of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr

School of Computer Science & Mathematics, Victoria University
Po Box 14428, Melbourne Vic 8001
Australia
sever.dragomir@vu.edu.au
URL:http://rgmia.vu.edu.au/dragomir

Faculty of Applied Technical Sciences, University of Prishtina,
Mother Theresa 5, 38 000 Prishtina
Kosova
razimhoxha@yahoo.com

Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb,
Croatia
pecaric@hazu.hr


Abstract:

There are many known reverses of the Cauchy-Bunyakovsky-Schwarz (CBS) inequality in the literature. We obtain here a general integral inequality comprising some of those results and also provide other related inequalities. The discrete case, which is of interest in its own turn, is also analysed.



12: Paper Source PDF document

Paper's Title:

Bounds for Two Mappings Associated to the Hermite-Hadamard Inequality

Author(s):

S. S. Dragomir1,2 and I. Gomm1

1Mathematics, School of Engineering & Science,
Victoria University,
PO Box 14428, Melbourne City, MC 8001,
Australia.

2School of Computational & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.

sever.dragomir@vu.edu.au
ian.gomm@vu.edu.au
URL: http://rgmia.org/dragomir  
 

Abstract:

Some inequalities concerning two mappings associated to the celebrated Hermite-Hadamard integral inequality for convex function with applications for special means are given.



12: Paper Source PDF document

Paper's Title:

Some Applications of Fejér's Inequality for Convex Functions (I)

Author(s):

S.S. Dragomir1,2 and I. Gomm1

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia.

sever.dragomir@vu.edu.au

URL: http://rgmia.org/dragomir

2School of Computational & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.

Abstract:

Some applications of Fejér's inequality for convex functions are explored. Upper and lower bounds for the weighted integral

under various assumptions for f with applications to the trapezoidal quadrature rule are given. Some inequalities for special means are also provided



12: Paper Source PDF document

Paper's Title:

Some New Generalizations of Jensen's Inequality with Related Results and Applications

Author(s):

Steven G. From

Department of Mathematics
University of Nebraska at Omaha
Omaha, Nebraska 68182-0243.

E-mail: sfrom@unomaha.edu

Abstract:

In this paper, some new generalizations of Jensen's inequality are presented. In particular, upper and lower bounds for the Jensen gap are given and compared analytically and numerically to previously published bounds for both the discrete and continuous Jensen's inequality cases. The new bounds compare favorably to previously proposed bounds. A new method based on a series of locally linear interpolations is given and is the basis for most of the bounds given in this paper. The wide applicability of this method will be demonstrated. As by-products of this method, we shall obtain some new Hermite-Hadamard inequalities for functions which are 3-convex or 3-concave. The new method works to obtain bounds for the Jensen gap for non-convex functions as well, provided one or two derivatives of the nonlinear function are continuous. The mean residual life function of applied probability and reliability theory plays a prominent role in construction of bounds for the Jensen gap. We also present an exact integral representation for the Jensen gap in the continuous case. We briefly discuss some inequalities for other types of convexity, such as convexity in the geometric mean, and briefly discuss applications to reliability theory.



11: Paper Source PDF document

Paper's Title:

Norm Estimates for the Difference between Bochner’s Integral and the Convex Combination of Function’s Values

Author(s):

P. Cerone, Y.J. Cho, S.S. Dragomir, J.K. Kim, and S.S. Kim

School of Computer Science and Mathematics,
Victoria University of Technology,
Po Box 14428, Mcmc 8001, Victoria, Australia.
pietro.cerone@vu.edu.au
URL
:
http://rgmia.vu.edu.au/cerone/index.html

Department of Mathematics Education, College of Education,
Gyeongsang National University, Chinju 660-701, Korea
yjcho@nongae.gsnu.ac.kr

School of Computer Science and Mathematics,
Victoria University of Technology,
Po Box 14428, Mcmc 8001, Victoria, Australia.
sever.dragomir@vu.edu.au
URL
:
http://rgmia.vu.edu.au/SSDragomirWeb.html

Department of Mathematics, Kyungnam University,
Masan,, Kyungnam 631-701, Korea
jongkyuk@kyungnam.ac.kr

Department of Mathematics, Dongeui University,
Pusan 614-714, Korea
sskim@dongeui.ac.kr

Abstract:

Norm estimates are developed between the Bochner integral of a vector-valued function in Banach spaces having the Radon-Nikodym property and the convex combination of function values taken on a division of the interval [a, b].



10: Paper Source PDF document

Paper's Title:

A Generalization of Ostrowski's Inequality for Functions of Bounded Variation via a Parameter

Author(s):

Seth Kermausuor

Department of Mathematics and Computer Science,
Alabama State University,
Montgomery, AL 36101,
USA.
E-mail: skermausour@alasu.edu

Abstract:

In this paper, we provide a generalization of the Ostrowski's inequality for functions of bounded variation for k points via a parameter λ∈[0,1]. As a by product, we consider some particular cases to obtained some interesting inequalities in these directions. Our results generalizes some of the results by Dragomir in [S. S. DRAGOMIR, The Ostrowski inequality for mappings of bounded variation, Bull. Austral. Math. Soc., 60 (1999), pp. 495--508.]



9: Paper Source PDF document

Paper's Title:

A Reverse of the Triangle Inequality in Inner Product Spaces and Applications for Polynomials

Author(s):

I. Brnetić, S. S. Dragomir, R. Hoxha and J. Pečarić

Department of Applied Mathematics, Faculty of Electrical Engineering and Computing,
University of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr

School of Computer Science & Mathematics, Victoria University
Po Box 14428, Melbourne Vic 8001
Australia
sever.dragomir@vu.edu.au
URL:http://rgmia.vu.edu.au/dragomir

Faculty of Applied Technical Sciences, University of Prishtina,
Mother Theresa 5, 38 000 Prishtina
Kosova
razimhoxha@yahoo.com

Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb,
Croatia
pecaric@hazu.hr


Abstract:

A reverse of the triangle inequality in inner product spaces related to the celebrated Diaz-Metcalf inequality with applications for complex polynomials is given.



9: Paper Source PDF document

Paper's Title:

Some New Inequalities of Hermite-Hadamard and Fejér Type for Certain Functions with Higher Convexity

Author(s):

Steven G. From

Department of Mathematics,
University of Nebraska at Omaha,
Omaha, Nebraska 68182-0243,
U.S.A.
E-mail: sfrom@unomaha.edu

Abstract:

In this paper, we present some new inequalities of Hermite-Hadamard or Fejér type for certain functions satisfying some higher convexity conditions on one or more derivatives.
An open problem is given also.
Some applications to the logarithmic mean are given.



8: Paper Source PDF document

Paper's Title:

Bounds on the Jensen Gap, and Implications for Mean-Concentrated Distributions

Author(s):

Xiang Gao, Meera Sitharam, Adrian E. Roitberg

Department of Chemistry, and Department of Computer & Information Science & Engineering,
University of Florida,
Gainesville, FL 32611,
USA.
E-mail: qasdfgtyuiop@gmail.com
URL: https://scholar.google.com/citations?user=t2nOdxQAAAAJ

Abstract:

This paper gives upper and lower bounds on the gap in Jensen's inequality, i.e., the difference between the expected value of a function of a random variable and the value of the function at the expected value of the random variable. The bounds depend only on growth properties of the function and specific moments of the random variable. The bounds are particularly useful for distributions that are concentrated around the mean, a commonly occurring scenario such as the average of i.i.d. samples and in statistical mechanics.



7: Paper Source PDF document

Paper's Title:

Generalizations of Hermite-Hadamard's Inequalities for Log-Convex Functions

Author(s):

Ai-Jun Li

School of Mathematics and Informatics, Henan Polytechnic University,
Jiaozuo City, Henan Province,
454010, China.
liaijun72@163.com


Abstract:

In this article, Hermite-Hadamard's inequalities are extended in terms of the weighted power mean and log-convex function. Several refinements, generalizations and related inequalities are obtained.



7: Paper Source PDF document

Paper's Title:

Several Applications of a Local Non-convex Young-type Inequality

Author(s):

Loredana Ciurdariu, Sorin Lugojan

Department of Mathematics,
"Politehnica" University of Timisoara,
P-ta. Victoriei, No.2, 300006-Timisoara,
Romania.

E-mail: ltirtirau87@yahoo.com

Abstract:

A local version of the Young inequality for positive numbers is used in order to deduce some inequalities about determinants and norms for real quadratic matrices and norms of positive operators on complex Hilbert spaces.



6: Paper Source PDF document

Paper's Title:

Refinement Inequalities Among Symmetric Divergence Measures

Author(s):

Inder Jeet Taneja

Departamento de Matemática,
Universidade Federal de Santa Catarina, 88.040-900
Florianópolis, Sc, Brazil

taneja@mtm.ufsc.br

URL: http://www.mtm.ufsc.br/~taneja

Abstract:

There are three classical divergence measures in the literature on information theory and statistics, namely, Jeffryes-Kullback-Leiber’s J-divergence, Sibson-Burbea-Rao’s Jensen- Shannon divegernce and Taneja’s arithemtic - geometric mean divergence. These bear an interesting relationship among each other and are based on logarithmic expressions. The divergence measures like Hellinger discrimination, symmetric χ2divergence, and triangular discrimination are not based on logarithmic expressions. These six divergence measures are symmetric with respect to probability distributions. In this paper some interesting inequalities among these symmetric divergence measures are studied. Refinements of these inequalities are also given. Some inequalities due to Dragomir et al. [6] are also improved.



5: Paper Source PDF document

Paper's Title:

Improvement of Jensen's Inequality for Superquadratic Functions

Author(s):

S. Abramovich, B. Ivanković, and J. Pečarić

Department of Mathematics,
University of Haifa,
Haifa 31905,
Israel.
abramos@math.haifa.ac.il

Faculty of Transport and Trafic Engineering,
University of Zagreb,
Vukelićeva 4, 10000,
Croatia
bozidar.ivankovic@zg.t-com.hr

Faculty of Textile,
University of Zagreb,
Prilaz Baruna Filipovića 30, 10000 Zagreb,
Croatia
pecaric@element.hr

 

Abstract:

Since 1907, the famous Jensen's inequality has been refined in different manners. In our paper, we refine it applying superquadratic functions and separations of domains for convex functions. There are convex functions which are not superquadratic and superquadratic functions which are not convex. For superquadratic functions which are not convex we get inequalities analogue to inequalities satisfied by convex functions. For superquadratic functions which are convex (including many useful functions) we get refinements of Jensen's inequality and its extensions.



5: Paper Source PDF document

Paper's Title:

Fejér-type Inequalities

Author(s):

Nicuşor Minculete and Flavia-Corina Mitroi

"Dimitrie Cantemir" University,
107 Bisericii Române Street, Braşov, 500068,
România
minculeten@yahoo.com 

University of Craiova, Department of Mathematics,
Street A. I. Cuza 13, Craiova, RO-200585,
Romania
fcmitroi@yahoo.com 
 

Abstract:

The aim of this paper is to present some new Fejér-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.



4: Paper Source PDF document

Paper's Title:

Reverses of the Triangle Inequality in Inner Product Spaces

Author(s):

Sever S. Dragomir

School of Computer Science and Mathematics,
Victoria University Of Technology,
PO Box 14428, Mcmc 8001,
Victoria, Australia.
sever@csm.vu.edu.au
Url: http://rgmia.vu.edu.au/SSDragomirWeb.html

Abstract:

Some new reverses for the generalised triangle inequality in inner product spaces are given. Applications in connection to the Schwarz inequality and for vector-valued integrals are provided as well.



4: Paper Source PDF document

Paper's Title:

A note on Inequalities due to Martins, Bennett and Alzer

Author(s):

József Sándor

Babeş-Bolyai University of Cluj, Department of Mathematics and Computer Sciences
Kogălniceanu Nr.1, Cluj-Napoca,
Romania.
jjsandor@hotmail.com
jsandor@member.ams.org


Abstract:

A short history of certain inequalities by Martins, Bennett as well as Alzer, is provided. It is shown that, the inequality of Alzer for negative powers [6], or Martin's reverse inequality [7] are due in fact to Alzer [2]. Some related results, as well as a conjecture, are stated.



4: Paper Source PDF document

Paper's Title:

Inequalities of Gamma Function Appearing in Generalizing Probability Sampling Design

Author(s):

Mohammadkheer M. Al-Jararha And Jehad M. Al-Jararha

Department of Mathematics,
Yarmouk University,
Irbid 21163,
Jordan.
E-mail: mohammad.ja@yu.edu.jo

Department of Statistics,
Yarmouk University,
Irbid 21163,
Jordan.
E-mail: jehad@yu.edu.jo

Abstract:

In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities can be used to generalize different probability distribution functions. Also, they can be used to generalize some statistical designs, e.g., the probability proportional to the size without replacement design.



4: Paper Source PDF document

Paper's Title:

Riemann-Stieltjes Integrals and Some Ostrowski Type Inequalities

Author(s):

W. G. Alshanti

Department of General Studies,
Jubail University College,
KSA.
E-mail: shantiw@ucj.edu.sa

Abstract:

In this article, we investigate new integral inequalities of Ostrowski's type of various functional aspects. For mapping's second derivative, we assume two cases, namely, L1 and L spaces. Moreover, for first derivative, we investigate two different characteristics, namely, bounded variation and locally Lipchitz continuity. Applications to special means and composite quadrature rules are also carried out.



3: Paper Source PDF document

Paper's Title:

Reverse of Martin's Inequality

Author(s):

Chao-Ping Chen, Feng Qi, and Sever S. Dragomir

Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University,
Jiaozuo City, Henan 454010, China
chenchaoping@sohu.com; chenchaoping@hpu.edu.cn 

Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University,
Jiaozuo City, Henan 454010, China
qifeng@hpu.edu.cn 
Url: http://rgmia.vu.edu.au/qi.html

School of Computer Science and Mathematics,
Victoria University of Technology,
P. O. Box 14428, Melbourne City Mc,
Victoria 8001, Australia
Sever.Dragomir@vu.edu.au 
Url: http://rgmia.vu.edu.au/SSDragomirWeb.html
 

Abstract:

In this paper, it is proved that

for all natural numbers n, and all real r < 0.



3: Paper Source PDF document

Paper's Title:

The successive approximations method and error estimation in terms of at most the first derivative for delay ordinary differential equations

Author(s):

Alexandru Mihai Bica

Department of Mathematics,
University of Oradea,
Str. Armatei Romane no.5,
410087, Oradea,
Romania
smbica@yahoo.com
abica@uoradea.ro


Abstract:

We present here a numerical method for first order delay ordinary differential equations, which use the Banach's fixed point theorem, the sequence of successive approximations and the trapezoidal quadrature rule. The error estimation of the method uses a recent result of P. Cerone and S.S. Dragomir about the remainder of the trapezoidal quadrature rule for Lipchitzian functions and for functions with continuous first derivative.



3: Paper Source PDF document

Paper's Title:

Some Inequalities for Gramian Normal Operators and for Gramian Self-Adjoint Operators in Pseudo-Hilbert Spaces

Author(s):

Loredana Ciurdariu


Department of Mathematics,"Politehnica" University of Timisoara,
P-ta. Victoriei, No.2, 300006-Timisoara,
ROMANIA
cloredana43@yahoo.com.

Abstract:

Several inequalities for gramian normal operators and for gramian self-adjoint operators in pseudo-Hilbert spaces are presented.



3: Paper Source PDF document

Paper's Title:

A-Normal Operators In Semi Hilbertian Spaces

Author(s):

A. Saddi

Department of Mathematics,
College of Education for Girls in Sarat Ebeidah 61914, Abha,
King Khalid University
Saudi Arabia
adel.saddi@fsg.rnu.tn
 

Abstract:

In this paper we study some properties and inequalities of A-normal operators in semi-Hilbertian spaces by employing some known results for vectors in inner product spaces. We generalize also most of the inequalities of (α,β)-normal operators discussed in Hilbert spaces [7].



3: Paper Source PDF document

Paper's Title:

On the Hyers-Ulam Stability of Homomorphisms and Lie Derivations

Author(s):

Javad Izadi and Bahmann Yousefi

Department of Mathematics, Payame Noor University,
P.O. Box: 19395-3697, Tehran,
Iran.
E-mail: javadie2003@yahoo.com, b_yousefi@pnu.ac.ir

 

Abstract:

Let A be a Lie Banach*-algebra. For each elements (a, b) and (c, d) in A2:= A * A, by definitions

 (a, b) (c, d)= (ac, bd),
 |(a, b)|= |a|+ |b|,
(a, b)*= (a*, b*),

A2 can be considered as a Banach*-algebra. This Banach*-algebra is called a Lie Banach*-algebra whenever it is equipped with the following definitions of Lie product:

for all a, b, c, d in A. Also, if A is a Lie Banach*-algebra, then D: A2→A2 satisfying

 D ([ (a, b), (c, d)])= [ D (a, b), (c, d)]+ [(a, b), D (c, d)]

for all $a, b, c, d∈A, is a Lie derivation on A2. Furthermore, if A is a Lie Banach*-algebra, then D is called a Lie* derivation on A2 whenever D is a Lie derivation with D (a, b)*= D (a*, b*) for all a, b∈A. In this paper, we investigate the Hyers-Ulam stability of Lie Banach*-algebra homomorphisms and Lie* derivations on the Banach*-algebra A2.



3: Paper Source PDF document

Paper's Title:

Hermite-Hadamard Type Inequalities for k-Riemann Liouville Fractional Integrals Via Two Kinds of Convexity

Author(s):

R. Hussain1, A. Ali2, G. Gulshan3, A. Latif4 and K. Rauf5

1,2,3,4Department of Mathematics,
Mirpur University of Science and Technology, Mirpur.
Pakistan.
E-mail1rashida12@gmail.com
E-mail2: unigraz2009@yahoo.com
E-mail3: ghazalagulshan@yahoo.com
E-mail4: asialatif87@gmail.com

5Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria.
E-mail5: krauf@unilorin.edu.ng

Abstract:

In this article, a fundamental integral identity including the first order derivative of a given function via k-Riemann-Liouville fractional integral is established. This is used to obtain further Hermite-Hadamard type inequalities involving left-sided and right-sided k-Riemann-Liouville fractional integrals for m-convex and (s,m)-convex functions respectively.



3: Paper Source PDF document

Paper's Title:

Some Inequalities of the Hermite-Hadamard Type for k-Fractional Conformable Integrals

Author(s):

C.-J. Huang, G. Rahman, K. S. Nisar, A. Ghaffar and F. Qi

Department of Mathematics, Ganzhou Teachers College,
Ganzhou 341000, Jiangxi,
China.
E-mail: hcj73jx@126.com , huangcj1973@qq.com

Department of Mathematics, Shaheed Benazir Bhutto University,
Sheringal, Upper Dir, Khyber Pakhtoonkhwa,
Pakistan.
E-mail: gauhar55uom@gmail.com

Department of Mathematics, College of Arts and Science at Wadi Aldawaser, 11991,
Prince Sattam Bin Abdulaziz University, Riyadh Region,
Kingdom of Saudi Arabia.
E-mail: n.sooppy@psau.edu.sa, ksnisar1@gmail.com

Department of Mathematical Science, Balochistan University of Information Technology,
Engineering and Management Sciences, Quetta,
Pakistan.
E-mail: abdulghaffar.jaffar@gmail.com

School of Mathematical Sciences, Tianjin Polytechnic University,
Tianjin 300387,
China; Institute of Mathematics,
Henan Polytechnic University, Jiaozuo 454010, Henan,
China.
E-mail: qifeng618@gmail.com, qifeng618@qq.com

 

Abstract:

In the paper, the authors deal with generalized k-fractional conformable integrals, establish some inequalities of the Hermite-Hadamard type for generalized k-fractional conformable integrals for convex functions, and generalize known inequalities of the Hermite-Hadamard type for conformable fractional integrals.



2: Paper Source PDF document

Paper's Title:

Error estimates for aproximations of the Fourier transform of functions in Lp spaces

Author(s):

A. Aglic Aljinovic and J. Pecaric

 

Department of Applied Mathematics,
Faculty of Electrical Engineering and Computing,
University Of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr


Faculty of Textile Technology,
University of Zagreb, Pierottijeva 6, 10000 Zagreb,
Croatia
pecaric@hazu.hr

 

Abstract:

New inequalities concerning the Fourier transform are given. Estimates of the difference between two Fourier transforms and even bounds to the associated numerical quadrature formulae are provided as well.



2: Paper Source PDF document

Paper's Title:

Weighted Generalization of the Trapezoidal Rule via Fink Identity

Author(s):

S. Kovač, J. Pečarić and A. Vukelić

Faculty of Geotechnical Engineering, University of Zagreb,
Hallerova aleja 7, 42000 Vara
ždin,
Croatia.
sanja.kovac@gtfvz.hr

Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb,
Croatia.
pecaric@hazu.hr

Faculty of Food Technology and Biotechnology, Mathematics department, University of Zagreb,
Pierottijeva 6, 10000 Zagreb,
Croatia.
avukelic@pbf.hr


Abstract:

The weighted Fink identity is given and used to obtain generalized weighted trapezoidal formula for n-time differentiable functions. Also, an error estimate is obtained for this formula.



2: Paper Source PDF document

Paper's Title:

On the Asymptotic Behavior of Solutions of Third Order Nonlinear Differential Equations

Author(s):

Ivan Mojsej and Alena Tartaľová

Institute of Mathematics,
Faculty of Science, P. J. Šafárik University,
Jesenná 5, 041 54 Košice,
Slovak Republic
ivan.mojsej@upjs.sk

Department of Applied Mathematics and Business Informatics,
Faculty of Economics, Technical University,
Nemcovej 32, 040 01 Košice,
Slovak Republic
alena.tartalova@tuke.sk


Abstract:

This paper is concerned with the asymptotic behavior of solutions of nonlinear differential equations of the third order with quasiderivatives. Mainly, we present the necessary and sufficient conditions for the existence of nonoscillatory solutions with specified asymptotic behavior as t tends to infinity. These conditions are presented as integral criteria and involve only the coefficients of investigated differential equations. In order to prove some of the results, we use a topological approach based on the Schauder fixed point theorem.



2: Paper Source PDF document

Paper's Title:

The Riemann-Stieltjes Integral on Time Scales

Author(s):

D. Mozyrska, E. Pawłuszewicz, D. Torres

Faculty Of Computer Science,
Białystok University Of Technology,
15-351 Białystok,
 Poland
 d.mozyrska@pb.edu.pl


 Department Of Mathematics,
University Of Aveiro,
3810-193 Aveiro,
Portugal
 ewa@ua.pt


 Department Of Mathematics,
University Of Aveiro,
3810-193 Aveiro,
Portugal
 delfim@ua.pt

 

Abstract:

We study the process of integration on time scales in the sense of Riemann-Stieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given



2: Paper Source PDF document

Paper's Title:

The Best Upper Bound for Jensen's Inequality

Author(s):

Vasile Cirtoaje


Department of Automatic Control and Computers
University of Ploiesti
Romania.


vcirtoaje@upg-ploiesti.ro.

Abstract:

In this paper we give the best upper bound for the weighted Jensen's discrete inequality applied to a convex function f defined on a closed interval I in the case when the bound depends on f, I and weights. In addition, we give a simpler expression of the upper bound, which is better than existing similar one.



2: Paper Source PDF document

Paper's Title:

On Generalized Triangle Inequality in p-Freéchet Spaces, 0<p<1

Author(s):

M. A. Latif

Department of Mathematics,
University of Hail, Hail,
Saudi Arabia
m_amer_latif@hotmail.com

Abstract:

In this paper generalized triangle inequality and its reverse in a p-Fréchet space where, 0<p<1 are obtained.



2: Paper Source PDF document

Paper's Title:

On Reformations of 2--Hilbert Spaces

Author(s):

M. Eshaghi Gordji, A. Divandari, M. R. Safi and Y. J. Cho

Department of Mathematics, Semnan University,
P.O. Box 35195--363, Semnan,
Iran

meshaghi@semnan.ac.ir, madjid.eshaghi@gmail.com

Department of Mathematics, Semnan University,
Iran

Divandari@sun.Semnan.ac.ir

Department of Mathematics, Semnan University,
Iran

safi@semnan.ac.ir, SafiMohammadReza@yahoo.com

Department of Mathematics Education and the RINS,
Gyeongsang National University
Chinju 660-701,
Korea

yjcho@gnu.ac.kr

Abstract:

In this paper, first, we introduce the new concept of (complex) 2--Hilbert spaces, that is, we define the concept of 2--inner product spaces with a complex valued 2--inner product by using the 2--norm. Next, we prove some theorems on Schwartz's inequality, the polarization identity, the parallelogram laws and related important properties. Finally, we give some open problems related to 2--Hilbert spaces.



2: Paper Source PDF document

Paper's Title:

An Improvement of the Hermite-Hadamard Inequality for Functions Convex on the Coordinates

Author(s):

Milica Klaričić Bakula

Faculty of Science,
University of Split,
Teslina 12, 21000 Split.
Croatia

E-mail: milica@pmfst.hr

Abstract:

An improvement of the Hermite-Hadamard inequality for functions convex on the coordinates is given.



2: Paper Source PDF document

Paper's Title:

Birkhoff-James orthogonality and Best Approximant in L1(X)

Author(s):

Mecheri Hacene and Rebiai Belgacem

Department of Mathematics and Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
E-mail: mecherih2000@yahoo.fr

Department of Mathematics and Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
E-mail: brebiai@gmail.com

Abstract:

Let X  be a complex Banach space and let (X,ρ) be a positive measure space. The Birkhoff-James orthogonality is a generalization of Hilbert space orthogonality to Banach spaces. We use this notion of orthogonality to establish a new characterization of Birkhoff-James orthogonality of bounded linear operators in L1(X,ρ) also implies best approximation has been proved.



1: Paper Source PDF document

Paper's Title:

New Proofs of the Grüss Inequality

Author(s):

A.Mc.D. Mercer and Peter R. Mercer

Dept. Mathematics and Statistics,
University of Guelph, Guelph, Ontario,
Canada.
amercer@reach.net

Dept. Mathematics,
S.U.N.Y. College at Buffalo, Buffalo, NY,
U.S.A.
mercerpr@math.buffalostate.edu

 


 

Abstract:

We present new proofs of the Grüss inequality in its original form and in its linear functional form.



1: Paper Source PDF document

Paper's Title:

Quantitative Estimates for Positive Linear Operators Obtained by Means of Piecewise Linear Functions

Author(s):

Vasile Mihesan

Technical University of Cluj-Napoca,
Department of Mathematics,
Str. C. Daicoviciu 15, Cluj-Napoca,
Romania
Vasile.Mihesan@math.utcluj.ro

 

Abstract:

In this paper we obtain estimates for the remainder in approximating continuous functions by positive linear operators, using piecewise linear functions.



1: Paper Source PDF document

Paper's Title:

On the Hohov Convolution Of The Class Sp(α,β)

Author(s):

T. N. Shanmugam and S. Sivasubramanian

Department of Mathematics,
Anna University,
Chennai 600025,
Tamilnadu, India.
shan@annauniv.edu

Department of Mathematics,
Easwari Engineering College,
Chennai-600089,
Tamilnadu, India,
sivasaisastha@rediffmail.com


Abstract:

Let F(a,b;c;z) be the Gaussian hypergeometric function and Ia,b;c(f)=zF(a,b;c;z)*f(z) be the Hohlov operator defined on the class A of all normalized analytic functions. We determine conditions on the parameters a,b,c such that Ia,b;c(f) will be in the class of parabolic starlike functions Sp(α,β). Our results extend several earlier results.



1: Paper Source PDF document

Paper's Title:

Solution of the Hyers-Ulam Stability Problem for Quadratic Type Functional Equations in Several Variables

Author(s):

John Michael Rassias

Pedagogical Department, E.E., National and Capodistrian University of Athens,
Section of Mathematics and Informatics,
4, Agamemnonos Str., Aghia Paraskevi,
Athens 15342,
Greece jrassias@primedu.uoa.gr
URL: http://www.primedu.uoa.gr/~jrassias/


Abstract:

In 1940 (and 1968) S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D. H. Hyers solved the Hyers-Ulam problem for linear mappings. In 1951 D. G. Bourgin has been the second author treating the Ulam problem for additive mappings. In 1978 according to P. M. Gruber this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types. In 1982-2004 we established the Hyers-Ulam stability for the Ulam problem for different mappings. In this article we solve the Hyers-Ulam problem for quadratic type functional equations in several variables. These stability results can be applied in stochastic analysis, financial and actuarial mathematics, as well as in psychology and sociology.



1: Paper Source PDF document

Paper's Title:

Parameter dependence of the solution of second order nonlinear ODE's via Perov's fixed point theorem

Author(s):

A. M. Bica, S. Muresan and G. Grebenisan

University of Oradea,
Str. Armatei Romane no.5, 410087,
Oradea, Romania.
smbica@yahoo.com
smuresan@uoradea.ro
grebe@uoradea.ro


Abstract:

Using the Perov's fixed point theorem, the smooth dependence by parameter of the solution of a two point boundary value problem corresponding to nonlinear second order ODE's is obtained.



1: Paper Source PDF document

Paper's Title:

Notes on Sakaguchi Functions

Author(s):

Shigeyoshi Owa, Tadayuki Sekine and Rikuo Yamakawa

Department of Mathematics, Kinki University,
Higashi-Osaka, Osaka 577-8502,
Japan.
owa@math.kindai.ac.jp

Office of Mathematics, College of Pharmacy, Nihon University,
7-1 Narashinodai, Funabashi-city,
Chiba, 274-8555, Japan.
tsekine@pha.nihon-u.ac.jp

Department of Mathematics, Shibaura Institute of Technology,
Minuma, Saitama-city,
Saitama 337-8570, Japan.
yamakawa@sic.shibaura-it.ac.jp


Abstract:

By using the definition for certain univalent functions f(z) in the open unit disk U given by K. Sakaguchi [2], two classes S(α) and T(α) of analytic functions in U are introduced. The object of the present paper is to discuss some properties of functions f(z) belonging to the classes S(α) and T(α).



1: Paper Source PDF document

Paper's Title:

Coincidences and Fixed Points of Hybrid Maps in Symmetric Spaces

Author(s):

S. L. Singh and Bhagwati Prasad

Vedic MRI, 21 Govind Nagar,
Rishikesh 249201
India
vedicmri@gmail.com

Department of Mathematics, Gurukula Kangri University,
Hardwar 249404,
India


Abstract:

The purpose of this paper is to obtain a new coincidence theorem for a single-valued and two multivalued operators in symmetric spaces. We derive fixed point theorems and discuss some special cases and applications.



1: Paper Source PDF document

Paper's Title:

Existence of solutions for Neutral Stochastic Functional Differential Systems with Infinite Delay in Abstract Space

Author(s):

P. Balasubramaniam, A. V. A. Kumar and S. K. Ntouyas

Department of Mathematics, Gandhigram Rural Institute,
Deemed University, Gandhigram - 624 302, Tamil Nadu, India.
pbalgri@rediffmail.com

Department of Mathematics, Gandhigram Rural Institute,
Deemed University, Gandhigram - 624 302, Tamil Nadu, India.
nnddww@tom.com

Department of Mathematics, University of Ioannina,
451 10 Ioannina,
Greece.
sntouyas@cc.uoi.gr
URL: http://www.math.uoi.gr/~sntouyas


Abstract:

In this paper we prove existence results for semilinear stochastic neutral functional differential systems with unbounded delay in abstract space. Our theory makes use of analytic semigroups and fractional power of closed operators and Sadovskii fixed point theorem.



1: Paper Source PDF document

Paper's Title:

A Coefficient Inequality For Certain Subclasses of Analytic Functions Related to Complex Order

Author(s):

B. Srutha Keerthi, B. Adolf Stephen and S. Sivasubramanian

Department Of Applied Mathematics, Sri Venkateswara College Of Engineering, Anna University,
Sriperumbudur, Chennai - 602 105,
India.
laya@svce.ac.in

Department of Mathematics, Madras Christian College, Chennai - 600059,
India
adolfmcc2003@yahoo.co.in

Department of Mathematics, College of Engineering, Anna University,
Tamilnadu, Chennai - 600 025,
India.
sivasaisastha@rediffmail.com


Abstract:

In this present investigation, the authors obtain coefficient inequality for certain normalized analytic functions of complex order f(z) defined on the open unit disk for which ( and be a complex number) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions of complex order defined by convolution are given. As a special case of this result, coefficient inequality for a class of functions defined through fractional derivatives is obtained. The motivation of this paper is to give a generalization of the coefficient inequalities of the subclasses of starlike and convex functions of complex order.



1: Paper Source PDF document

Paper's Title:

Product Formulas Involving Gauss Hypergeometric Functions

Author(s):

Edward Neuman

Department of Mathematics, Mailcode 4408,
Southern Illinois University,
1245 Lincoln Drive,
Carbondale, IL 62901,
USA.
edneuman@math.siu.edu
URL: http://www.math.siu.edu/neuman/personal.html


Abstract:

New formulas for a product of two Gauss hypergeometric functions are derived. Applications to special functions, with emphasis on Jacobi polynomials, Jacobi functions, and Bessel functions of the first kind, are included. Most of the results are obtained with the aid of the double Dirichlet average of a univariate function.



1: Paper Source PDF document

Paper's Title:

On Interaction of Discontinuous Waves in a Gas with Dust Particles

Author(s):

J. Jena

Department of Mathematics, Netaji Subhas institute of technology,
Sector-3, Dwarka, New Delhi - 110 075,
India.
jjena67@rediffmail.com
jjena@nsit.ac.in


Abstract:

In this paper, the interaction of the strong shock with the weak discontinuity has been investigated for the system of partial differential equations describing one dimensional unsteady plane flow of an inviscid gas with large number of dust particles. The amplitudes of the reflected and transmitted waves after interaction of the weak discontinuity through a strong shock are evaluated by exploiting the results of general theory of wave interaction.



1: Paper Source PDF document

Paper's Title:

Existence of Large Solutions to Non-Monotone Semilinear Elliptic Equations

Author(s):

Alan V. Lair, Zachary J. Proano, and Aihua W. Wood

Air Force Institute of Technology
2950 Hobson Way, AFIT/ENC
Wright-Patterson Air Force Base, OH, 45433-7765,
USA.
Aihua.Wood@afit.edu
URL: www.afit.edu


Abstract:

We study the existence of large solutions of the semilinear elliptic equation Δu=p(x)f(u) where f is not monotonic. We prove existence, on bounded and unbounded domains, under the assumption that f is Lipschitz continuous, f(0) = 0, f(s) > 0 for s > 0 and there exists a nonnegative, nondecreasing Hölder continuous function g and a constant M such that g(s) ≤ f(s) ≤ Mg(s) for large s. The nonnegative function p is allowed to be zero on much of the domain.



1: Paper Source PDF document

Paper's Title:

On a Subclass of Uniformly Convex Functions Defined by the Dziok-Srivastava Operator

Author(s):

M. K. Aouf and G. Murugusundaramoorthy

Mathematics Department, Faculty of Science,
Mansoura University 35516,
Egypt.
mkaouf127@yahoo.com

School of Science and Humanities, VIT University
Vellore - 632014,
India.
gmsmoorthy@yahoo.com


Abstract:

Making use of the Dziok-Srivastava operator, we define a new subclass Tlm([α1];α,β) of uniformly convex function with negative coefficients. In this paper, we obtain coefficient estimates, distortion theorems, locate extreme points and obtain radii of close-to-convexity, starlikeness and convexity for functions belonging to the class Tlm([α1];α,β) . We consider integral operators associated with functions belonging to the class Hlm([α1];α,β) defined via the Dziok-Srivastava operator. We also obtain several results for the modified Hadamard products of functions belonging to the class Tlm([α1];α,β) and we obtain properties associated with generalized fractional calculus operators.



1: Paper Source PDF document

Paper's Title:

On Stable Numerical Differentiation

Author(s):

N. S. Hoang and A. G. Ramm

Mathematics Department, Kansas State University
Manhattan, KS 66506-2602,
U. S. A.
nguyenhs@math.ksu.edu
ramm@math.ksu.edu
URL:http://math.ksu.edu/~ramm

Abstract:

Based on a regularized Volterra equation, two different approaches for numerical differentiation are considered. The first approach consists of solving a regularized Volterra equation while the second approach is based on solving a disretized version of the regularized Volterra equation. Numerical experiments show that these methods are efficient and compete favorably with the variational regularization method for stable calculating the derivatives of noisy functions.



1: Paper Source PDF document

Paper's Title:

Existence of Bounded Solutions for a Class of Strongly Nonlinear Elliptic Equations in Orlicz-Sobolev Spaces

Author(s):

Abdelmoujib Benkirane and Ahmed Youssfi

Department of Mathematics and Informatics, Faculty of Sciences Dhar El Mahraz
University Sidi Mohammed Ben Abdallah
PB 1796 Fez-Atlas, Fez
Morocco
a.benkirane@menara.ma
ahmed.youssfi@caramail.com


Abstract:

We prove, in the setting of Orlicz-Sobolev spaces, the existence of bounded solutions for some strongly nonlinear elliptic equations with operator of the principal part having degenerate coercivity and lower order terms not satisfying the sign condition. The data have a suitable summability and no Δ2-condition is needed for the considered N-functions.



1: Paper Source PDF document

Paper's Title:

Positive Solutions for Systems of Three-point Nonlinear Boundary Value Problems

Author(s):

J. Henderson and S. K. Ntouyas

Department of Mathematics, Baylor University
Waco, Texas
76798-7328 USA.
Johnny_Henderson@baylor.edu
URL: http://www3.baylor.edu/~Johnny_Henderson

Department of Mathematics, University of Ioannina
451 10 Ioannina,
Greece.
sntouyas@cc.uoi.gr
URL: http://www.math.uoi.gr/~sntouyas


Abstract:

Values of λ are determined for which there exist positive solutions of the system of three-point boundary value problems, u''(t)+ λa(t)f(v(t))=0, v''(t)+λb(t)g(u(t))=0, for 0 < t <1, and satisfying, u(0) = 0, u(1)=α u(η), v(0) = 0, v(1)=α v(η). A Guo-Krasnosel'skii fixed point theorem is applied.



1: Paper Source PDF document

Paper's Title:

Error Inequalities for Weighted Integration Formulae and Applications

Author(s):

Nenad Ujević and Ivan Lekić

Department of Mathematics
University of Split
Teslina 12/III, 21000 Split
CROATIA.
ujevic@pmfst.hr
ivalek@pmfst.hr


Abstract:

Weighted integration formulae are derived. Error inequalities for the weighted integration formulae are obtained. Applications to some special functions are also given.



1: Paper Source PDF document

Paper's Title:

Some Properties of the Solution of a Second Order Elliptic Abstract Differential Equation

Author(s):

A. Aibeche and K. Laidoune

Mathematics Department, Faculty of Sciences, University Ferhat Abbas, Setif,
Route de Scipion, 19000, Setif,
Algeria
aibeche@univ-setif.dz

Abstract:

In this paper we study a class of non regular boundary value problems for elliptic differential-operator equation of second order with an operator in boundary conditions. We give conditions which guarantee the coerciveness of the solution of the considered problem, the completeness of system of root vectors in Banach-valued functions spaces and we establish the Abel basis property of this system in Hilbert spaces. Finally, we apply this abstract results to a partial differential equation in cylindrical domain.



1: Paper Source PDF document

Paper's Title:

Hyers-Ulam-Rassias Stability of a Generalized Jensen Functional Equation

Author(s):

A. Charifi, B. Bouikhalene, E. Elqorachi and A. Redouani

Department of
Mathematics, Faculty of Sciences,
Ibn Tofail University,
Kenitra, Morocco
charifi2000@yahoo.fr bbouikhalene@yahoo.fr

Department of
Mathematics, Faculty of Sciences,
Ibn Zohr University,
Agadir, Morocco
elqorachi@hotmail.com Redouani-ahmed@yahoo.fr
 

Abstract:

In this paper we obtain the Hyers-Ulam-Rassias stability for the generalized Jensen's functional equation in abelian group (G,+). Furthermore we discuss the case where G is amenable and we give a note on the Hyers-Ulam-stability of the K-spherical (n × n)-matrix functional equation.



1: Paper Source PDF document

Paper's Title:

Superquadracity, Bohr's Inequality and Deviation from a Mean Value

Author(s):

S. Abramovich, J. Barić, and J. Pečarić

Department of Mathematics, University of Haifa,
Haifa, 31905,
Israel

abramos@math.haifa.ac.il
 

FESB, University of Split,
Rudera Bošcovića,
B.B., 21000, Split,
Croatia
jbaric@fesb.hr
 

Faculty of Textile Technology, University of Zagreb,
Prilaz Baruna Filipovića,
30, 10000 Zagreb,
Croatia.
pecaric@hazu.hr
 

Abstract:

Extensions of Bohr's inequality via superquadracity are obtained, where instead of the power p=2 which appears in Bohr's inequality we get similar results when we deal with p≥ 2 and with p≤ 2. Also, via superquadracity we extend a bound for deviation from a Mean Value.



1: Paper Source PDF document

Paper's Title:

The Superstability of the Pexider Type Trigonometric Functional Equation

Author(s):

Gwang Hui Kim and Young Whan Lee

Department of Mathematics, Kangnam
University Yongin, Gyeonggi, 446-702, Korea.
 ghkim@kangnam.ac.kr


Department of Computer and Information Security
Daejeon University, Daejeon 300-716, Korea.
ywlee@dju.ac.kr
 

Abstract:

The aim of this paper is to investigate the stability problem for
the Pexider type (hyperbolic) trigonometric functional equation
f(x+y)+f(x+σy)=λg(x)h(y) under the conditions :
|f(x+y)+f(x+σy)- λg(x)h(y)|≤φ(x),
φ(y)
, and min {φ(x), φ (y)}.

As a consequence, we have generalized the results of stability for
the cosine(d'Alembert), sine, and the Wilson functional equations by J.
Baker, P. Găvruta, R. Badora and R. Ger, Pl.~Kannappan, and G.
H. Kim



1: Paper Source PDF document

Paper's Title:

Error Estimates for Approximations of the Laplace transform of Functions in Lp Spaces

Author(s):

Andrea Aglić Aljinović

Department of Applied Mathematics,
Faculty of Electrical Engineering and Computing,
University of Zagreb,
Unska 3, 10 000 Zagreb,
Croatia

andrea.aglic@fer.hr 


 

Abstract:

In this paper error estimates of approximations in complex domain for the Laplace transform are given for functions which vanish beyond a finite domain and whose derivatives belongs to Lp spaces. New inequalities concerning the Laplace transform, as well as estimates of the difference between the two Laplace transforms are presented and used to obtain two associated numerical rules and error bounds of their remainders.



1: Paper Source PDF document

Paper's Title:

On Generalization of Hardy-type Inequalities

Author(s):

K. Rauf, S. Ponnusamy and J. O. Omolehin  

Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria
krauf@unilorin.edu.ng

Department of Mathematics,
Indian Institute of Technology Madras,
Chennai- 600 036,
India
samy@iitm.ac.in

Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria
omolehin_joseph@yahoo.com

Abstract:

This paper is devoted to some new generalization of Hardy-type integral inequalities and the reversed forms. The study is to determine conditions on which the generalized inequalities hold using some known hypothesis. Improvement of some inequalities are also presented.



1: Paper Source PDF document

Paper's Title:

On A Conjecture of A Logarithmically Completely Monotonic Function

Author(s):

Valmir Krasniqi, Armend Sh. Shabani

Department of Mathematics,
University of Prishtina,
Republic of Kosova

E-mail: vali.99@hotmail.com  
armend_shabani@hotmail.com

Abstract:

In this short note we prove a conjecture, related to a logarithmically completely monotonic function, presented in [5]. Then, we extend by proving a more generalized theorem. At the end we pose an open problem on a logarithmically completely monotonic function involving q-Digamma function.



1: Paper Source PDF document

Paper's Title:

Some New Nonlinear Integro-Differential Inequalities of Gronwall-Bellman-Pachpatte Type

Author(s):

A. ABDELDAIM

Department of Mathematics and Computer Sciences,
Faculty of Science,
Port Said University, Port Said,
EGYPT.

Department of Mathematics,
Faculty of Science and Humanities,
Shaqra University, Dawadmi,
SAUDI ARABIA.

E-mail: ahassen@su.edu.sa
URL: http://faculty.ksu.edu.sa/DRABDELDAIM/Pages/Home.aspx

Abstract:

In this paper we establish some new nonlinear integro-differential inequalities of Gronwall-Bellman-Pachpatte type for function of one independent variable. The purpose of this paper is to extend certain results which proved by Pachpatte in [On some fundamental integrodifferential and integral inequalities, An. Sti. Univ. Al. I. Cuza, Iasi, Vol.23 (1977), 77-86]. The inequalities obtained here can be used in the theory of some new classes of nonlinear integro-differential equations. Some applications are also given to illustrate the usefulness of our results.



1: Paper Source PDF document

Paper's Title:

A Nonhomogeneous Subdiffusion Heat Equation

Author(s):

Joel-Arturo Rodriguez-Ceballos, Ana-Magnolia Marin, Ruben-Dario Ortiz

Instituto Tecnológico de Morelia,
Morelia, Michoacan,
Mexico

E-mail: joel@ifm.umich.mx

Universidad de Cartagena,
Campus San Pablo,
Cartagena de Indias, Bolivar,
Colombia

E-mail: amarinr@unicartagena.edu.co

E-mail:  joel@ifm.umich.mx

Abstract:

In this paper we consider a nonhomogeneous subdiffusion heat equation of fractional order with Dirichlet boundary conditions.



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Paper's Title:

Weak solutions of non coercive stochastic Navier-Stokes equations in R2

Author(s):

Wilhelm Stannat and Satoshi Yokoyama

Technische Universität Berlin,
Strasse des 17. Juni 136, 10623 Berlin,
Germany.

Graduate School of Mathematical Sciences,
The University of Tokyo,
Komaba, Tokyo 153-8914,
Japan.

E-mail: stannat@math.tu-berlin.de

E-mail: satoshi2@ms.u-tokyo.ac.jp

Abstract:

We prove existence of weak solutions of stochastic Navier-Stokes equations in R2 which do not satisfy the coercivity condition. The equations are formally derived from the critical point of some variational problem defined on the space of volume preserving diffeomorphisms in R2. Since the domain of our equation is unbounded, it is more difficult to get tightness of approximating sequences of solutions in comparison with the case of a bounded domain. Our approach is based on uniform a priori estimates on the enstrophy of weak solutions of the stochastic 2D-Navier-Stokes equations with periodic boundary conditions, where the periodicity is growing to infinity combined with a suitable spatial cutoff-technique.



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Paper's Title:

Examples of Fractals Satisfying the Quasihyperbolic Boundary Condition

Author(s):

Petteri Harjulehto and Riku Klén

Department of Mathematics and Statistics,
FI-20014 University of Turku,
Finland

E-mail: petteri.harjulehto@utu.fi

E-mail: riku.klen@utu.fi

Abstract:

In this paper we give explicit examples of bounded domains that satisfy the quasihyperbolic boundary condition and calculate the values for the constants. These domains are also John domains and we calculate John constants as well. The authors do not know any other paper where exact values of parameters has been estimated.



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Paper's Title:

Hermite-Hadamard-Fejer Type Inequalities for Harmonically s-convex Functions via Fractional Integrals

Author(s):

İmdat İşcan, Mehmet Kunt

Department of Mathematics,
Faculty of Sciences and Arts,
Giresun University, Giresun,
Turkey.
E-mail: imdat.iscan@giresun.edu.tr


Department of Mathematics,
Faculty of Sciences,
Karadeniz Technical University,
61080, Trabzon,
Turkey.
E-mail: mkunt@ktu.edu.tr

Abstract:

In this paper, some Hermite-Hadamard-Fejer type integral inequalities for harmonically s-convex functions in fractional integral forms have been obtained.



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Paper's Title:

On the Biharmonic Equation with Nonlinear Boundary Integral Conditions

Author(s):

R. Hamdouche and H. Saker

L.M.A. Department of Mathematics, Faculty of Sciences,
University of Badji Mokhtar,
P.O.Box 12. Annaba 23000,
Algeria.
E-mail: h_saker@yahoo.fr, hmdch.rahma16@gmail.com

 

Abstract:

In the present work, we deal with the biharmonic problems in a bounded domain in the plane with the nonlinear boundary integral conditions. After applying the Boundary integral method, a system of nonlinear boundary integral equations is obtained. The result show that when the nonlinearity satisfies some conditions lead the existence and uniqueness of the solution.



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Paper's Title:

Hyponormal and K-Quasi-Hyponormal Operators On Semi-Hilbertian Spaces

Author(s):

Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali

Mathematics Department,
College of Science,
Aljouf University,
Aljouf 2014,
Saudi Arabia.
E-mail: sididahmed@ju.edu.sa

Mathematics Department, Faculty of Science,
Hassiba Benbouali, University of Chlef,
B.P. 151 Hay Essalem, Chlef 02000,
Algeria.
E-mail: benali4848@gmail.com

Abstract:

Let H be a Hilbert space and let A be a positive bounded operator on H. The semi-inner product < u|v>A:=<Au|v>, u,v H induces a semi-norm || .||A on H. This makes H into a semi-Hilbertian space. In this paper we introduce the notions of hyponormalities and k-quasi-hyponormalities for operators on semi Hilbertian space (H,||.||A), based on the works that studied normal, isometry, unitary and partial isometries operators in these spaces. Also, we generalize some results which are already known for hyponormal and quasi-hyponormal operators. An operator T BA (H) is said to be (A, k)-quasi-hyponormal if



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Paper's Title:

Partial Semigroup Algebras Associated to Partial Action

Author(s):

Bahman Tabatabaie Shourijeh and Sahar Moayeri Rahni

Department of Mathematics,
College of Sciences, Shiraz University,
Shiraz, 71454,
Iran.
E-mail: tabataba@math.susc.ac.ir

Department of Mathematics,
College of Sciences, Shiraz University,
Shiraz, 71454,
Iran.
E-mail: smoayeri@shirazu.ac.ir

Abstract:

For a given inverse semigroup S, we introduce the notion of algebraic crossed product by using a given partial action of S, and we will prove that under some condition it is associative. Also we will introduce the concept of partial semigroup algebra KPar(S), and we show that the suitable quotient of KPar(S) is a kind of crossed product.



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Paper's Title:

Strong Convergence Theorem for a Common Fixed Point of an Infinite Family of J-nonexpansive Maps with Applications

Author(s):

Charlse Ejike Chidume, Otubo Emmanuel Ezzaka and Chinedu Godwin Ezea

African University of Science and Technology,
Abuja,
Nigeria.
E-mail: cchidume@aust.edu.ng

Ebonyi State University,
Abakaliki,
Nigeria.
E-mail: mrzzaka@yahoo.com

 Nnamdi Azikiwe University,
Awka,
Nigeria.
E-mail: chinedu.ezea@gmail.com

Abstract:

Let E be a uniformly convex and uniformly smooth real Banach space with dual space E*. Let {Ti}i=1 be a family of J-nonexpansive maps, where, for each i,~Ti maps E to 2E*. A new class of maps, J-nonexpansive maps from E to E*, an analogue of nonexpansive self maps of E, is introduced. Assuming that the set of common J-fixed points of {Ti}i=1 is nonempty, an iterative scheme is constructed and proved to converge strongly to a point x* in n=1FJTi. This result is then applied, in the case that E is a real Hilbert space to obtain a strong convergence theorem for approximation of a common fixed point for an infinite family of nonexpansive maps, assuming existences. The theorem obtained is compared with some important results in the literature. Finally, the technique of proof is also of independent interest.



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Paper's Title:

Ostrowski Type Fractional Integral Inequalities for Generalized (s,m,φ)-preinvex Functions

Author(s):

Artion Kashuri and Rozana Liko

University of Vlora "Ismail Qemali",
Faculty of Technical Science,
Department of Mathematics, 9400,
Albania.
E-mail: artionkashuri@gmail.com
E-mail: rozanaliko86@gmail.com

Abstract:

In the present paper, the notion of generalized (s,m,φ)-preinvex function is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi type quadrature formula involving generalized (s,m,φ)-preinvex functions along with beta function are given. Moreover, some generalizations of Ostrowski type inequalities for generalized (s,m,φ)-preinvex functions via Riemann-Liouville fractional integrals are established.



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Paper's Title:

Convergence and Stability Results for New Three Step Iteration Process in Modular Spaces

Author(s):

Naresh Kumar and Renu Chugh

Department of Mathematics,
M.D. University,
Rohtak-124001, Haryana,
India.
E-mail: nks280@gmail.com
E-mail: chugh.r1@gmail.com

Abstract:

The aim of this paper is to introduce a new iteration process (5) for ρ-contraction mappings in Modular spaces. We obtain some analytical proof for convergence and stability of our iteration process (5). We show that our iteration process (5) gives faster convergence results than the leading AK iteration process (4) for contraction mappings. Moreover, a numerical example (using the Matlab Software) is presented to compare the rate of convergence for existing iteration processes with our new iteration process (5).



1: Paper Source PDF document

Paper's Title:

On Commutator of Aluthge Transforms and Fuglede-Putnam Property

Author(s):

(Manzar Maleki, Ali Reza Janfada and Seyed Mohammad Sadegh Nabavi Sales

International Campus, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad,
Iran.
E-mail: manzar.maleki@gmail.com
 

Faculty of Mathematics and Statistics, Department of Mathematics,
University of Birjand,
P. O. Box 414, Birjand 9717851367,
Iran.
E-mail: ajanfada@birjand.ac.ir

Department of Pure Mathematics, Hakim Sabzevari University,
P.O. Box 397, Sabzevar,
Iran.
E-mail: sadegh.nabavi@hsu.ac.ir

Abstract:

We deal with the well-known Fuglede-Putnam theorem and related FP-property. We show that if (A,B) has the FP-property, then so has where 0 t1,t21 are arbitrary. We first prove that if and only if AX=XB for all X, whenever (A,B) has the FP-property. We prove some similar results for instead of $ as well. Also we introduce the sequence of generalized iterations of Aluthge transform of operators and express some results for this notion associated to the FP-property.



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Paper's Title:

On Closed Range C*-modular Operators

Author(s):

Javad Farokhi-Ostad and Ali Reza Janfada

Department of Mathematics,
Faculty of Mathematics and Statistics Sciences,
University of Birjand, Birjand,
Iran.
E-mail: j.farokhi@birjand.ac.ir ajanfada@birjand.ac.ir

Abstract:

In this paper, for the class of the modular operators on Hilbert C*-modules, we give the conditions to closedness of their ranges. Also, the equivalence conditions for the closedness of the range of the modular projections on Hilbert C*-modules are discussed. Moreover, the mixed reverse order law for the Moore-Penrose invertible modular operators are given.



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Paper's Title:

Iterative Algorithm for Split Generalized Mixed Equilibrium Problem Involving Relaxed Monotone Mappings in Real Hilbert Spaces

Author(s):

1U.A. Osisiogu, F.L. Adum, and 2C. Izuchukwu

1Department of Mathematics and Computer Science,
Ebonyi State University, Abakaliki,
Nigeria.
E-mail: uosisiogu@gmail.com, adumson2@yahoo.com

2School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: izuchukwuc@ukzn.ac.za, izuchukwu_c@yahoo.com

Abstract:

The main purpose of this paper is to introduce a certain class of split generalized mixed equilibrium problem involving relaxed monotone mappings. To solve our proposed problem, we introduce an iterative algorithm and obtain its strong convergence to a solution of the split generalized mixed equilibrium problems in Hilbert spaces. As special cases of the proposed problem, we studied the proximal split feasibility problem and variational inclusion problem.



1: Paper Source PDF document

Paper's Title:

An Existence of the Solution to Neutral Stochastic Functional Differential Equations Under the Holder Condition

Author(s):

Young-Ho Kim

Department of Mathematics,
Changwon National University,
Changwon, Gyeongsangnam-do 51140,
Korea.

E-mail: iyhkim@changwon.ac.kr

Abstract:

In this paper, we show the existence and uniqueness of solution of the neutral stochastic functional differential equations under weakened H\"{o}lder condition, a weakened linear growth condition, and a contractive condition. Furthermore, in order to obtain the existence of a solution to the equation we used the Picard sequence.



1: Paper Source PDF document

Paper's Title:

Some fixed point results in partial S-metric spaces

Author(s):

M. M. Rezaee, S. Sedghi, A. Mukheimer, K. Abodayeh, and Z. D. Mitrovic

Department of Mathematics, Qaemshahr Branch,
Islamic Azad University, Qaemshahr,
Iran.
E-mail: Rezaee.mohammad.m@gmail.com

Department of Mathematics, Qaemshahr Branch,
Islamic Azad University, Qaemshahr,
Iran.
E-mail: sedghi.gh@qaemiau.ac.ir

Department of Mathematics and General Sciences,
Prince Sultan University, Riyadh,
KSA.
E-mail: mukheimer@psu.edu.sa

Department of Mathematics and General Sciences,
Prince Sultan University, Riyadh,
KSA.
E-mail: kamal@psu.edu.sa

Nonlinear Analysis Research Group,
Faculty of Mathematics and Statistics,
Ton Duc Thang University, Ho Chi Minh City,
Vietnam.
E-mail: zoran.mitrovic@tdtu.edu.vn

Abstract:

We introduce in this article a new class of generalized metric spaces, called partial S-metric spaces. In addition, we also give some interesting results on fixed points in the partial S-metric spaces and some applications.



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Paper's Title:

Composite Variational-Like Inequalities Given By Weakly Relaxed ζ-Semi-Pseudomonotone Multi-Valued Mapping

Author(s):

Syed Shakaib Irfan, Iqbal Ahmad, Zubair Khan and Preeti Shukla

College of Engineering, Qassim University
Buraidah, Al-Qassim,
Saudi Arabia.
E-mail: shakaib@qec.edu.sa

College of Engineering, Qassim University
Buraidah, Al-Qassim,
Saudi Arabia.
E-mail: iqbal@qec.edu.sa

Department of Mathematics,
Integral University Lucknow,
India.
E-mail: zkhan@iul.ac.in

Department of Mathematics,
Integral University Lucknow,
India.
E-mail: shuklapreeti1991@gmail.com

 

Abstract:

In this article, we introduce a composite variational-like inequalities with weakly relaxed ζ-pseudomonotone multi-valued maping in reflexive Banach spaces. We obtain existence of solutions to the composite variational-like inequalities with weakly relaxed ζ-pseudomon -otone multi-valued maps in reflexive Banach spaces by using KKM theorem. We have also checked the solvability of the composite variational-like inequalities with weakly relaxed ζ-semi-pseudomonotone multi-valued maps in arbitrary Banach spaces using Kakutani-Fan-Glicksberg fixed point theorem.



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Paper's Title:

Double Difference of Composition Operator on Bloch Spaces

Author(s):

Rinchen Tundup

Department of Mathematics
University of Jammu
Jammu and Kashmir
India.

E-mail: joneytun123@gmail.com

Abstract:

In this paper we characterize the compactness of double difference of three non-compact composition operators on Bloch space induced by three holomorphic self maps on the unit disc.



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Paper's Title:

Attempts to Define a Baum--Connes Map Via Localization of Categories for Inverse Semigroups

Author(s):

Bernhard Burgstaller

Departamento de Matematica,
Universidade Federal de Santa Catarina,
CEP 88.040-900 Florianopolis-SC,
Brasil.
E-mail: bernhardburgstaller@yahoo.de
URL: http://mathematik.work/bernhardburgstaller/index.html

Abstract:

An induction functor in inverse semigroup equivariant KK-theory is considered, and together with %a restriction functors certain results similar to those known from the Mackey machinery are shown. It is also verified that for any so-called E-continuous inverse semigroup its equivariant KK-theory satisfies the universal property and is a triangulated category.



1: Paper Source PDF document

Paper's Title:

Estimates of Norms on Krein Spaces

Author(s):

Satheesh K. Athira, P. Sam Johnson and K. Kamaraj

Department of Mathematical and Computational Sciences,
National Institute of Technology Karnataka,
Surathkal, Mangaluru 575 025,
India.
E-mail: athirachandri@gmail.com

Department of Mathematical and Computational Sciences,
National Institute of Technology Karnataka,
Surathkal, Mangaluru 575 025,
India.
E-mail:sam@nitk.edu.in

Department of Mathematics,
University College of Engineering Arni,
Anna University, Arni 632 326,
India.
E-mail: krajkj@yahoo.com

Abstract:

Various norms can be defined on a Krein space by choosing different underlying fundamental decompositions. Some estimates of norms on Krein spaces are discussed and a few results in Bognar's paper are generalized.



1: Paper Source PDF document

Paper's Title:

Sharp Inequalities Between Hölder and Stolarsky Means of Two Positive Numbers

Author(s):

M. Bustos Gonzalez and A. I. Stan

The University of Iowa,
Department of Mathematics,
14 MacLean Hall,
Iowa City, Iowa,
USA.
E-mail: margarita-bustosgonzalez@uiowa.edu
 
The Ohio State University at Marion,
Department of Mathematics,
1465 Mount Vernon Avenue,
Marion, Ohio,
USA.
E-mail: stan.7@osu.edu

Abstract:

Given any index of the Stolarsky means, we find the greatest and least indexes of the H\"older means, such that for any two positive numbers, the Stolarsky mean with the given index is bounded from below and above by the Hölder means with those indexes, of the two positive numbers. Finally, we present a geometric application of this inequality involving the Fermat-Torricelli point of a triangle.


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