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64: 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.



63: 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.



48: 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.



39: 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.



24: 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.



20: Paper Source PDF document

Paper's Title:

Hardy Type Inequalities via Convexity - The Journey so Far

Author(s):

 James A. Oguntuase and Lars-Erik Persson

 Department of Mathematics, University of Agriculture,
 P. M. B. 2240, Abeokuta, Nigeria.

Department of Mathematics, Luleå University of Technology,
SE-971 87, Luleå , Sweden.

oguntuase@yahoo.com, larserik@sm.luth.se .
 

Abstract:

It is nowadays well-known that Hardy's inequality (like many other inequalities) follows directly from Jensen's inequality. Most of the development of Hardy type inequalities has not used this simple fact, which obviously was unknown by Hardy himself and many others. Here we report on some results obtained in this way mostly after 2002 by mainly using this fundamental idea.  



16: 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.



16: 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.



13: 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.



13: 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.



10: 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



10: Paper Source PDF document

Paper's Title:

New Refinements of Hölder's Inequality

Author(s):

Xiu-Fen Ma

College of Mathematical and Computer,
Chongqing Normal University Foreign Trade and Business College,
No.9 of Xuefu Road, Hechuan District 401520,
Chongqing City,
The People's Republic of China.
E-mail: maxiufen86@163.com

Abstract:

In this paper, we define two mappings, investigate their properties, obtain some new refinements of Hölder's inequality.



9: 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.



7: Paper Source PDF document

Paper's Title:

Ulam Stability of Functional Equations

Author(s):

Stefan Czerwik and Krzysztof Król

Institute of Mathematics
 Silesian University of Technology
 Kaszubska 23, 44-100 Gliwice,
Poland

Stefan.Czerwik@polsl.pl
Krzysztof.Krol@polsl.pl

Abstract:

In this survey paper we present some of the main results on Ulam-Hyers-Rassias stability for important functional equations.



7: 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.



6: Paper Source PDF document

Paper's Title:

Stability of a Pexiderized Equation

Author(s):

Maryam Amyar

Department of Mathematics,
Islamic Azad University, Rahnamaei Ave,
Mashhad 91735, Iran,
and Banach Mathematical Research Group (BMRG)
amyari@mshdiau.ac.ir

URL: http://amyari.mshdiau.ac.ir


Abstract:

The aim of the paper is to prove the stability of the Pexiderized equation f(x)=g(y+x)-h(y-x), for any amenable abelian group.



5: 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:

On an Integral Inequality of the Hardy-Type

Author(s):

C. O. Imoru and A. G. Adeagbo-Sheikh

Department of Mathematics
Obafemi Awolowo University, Ile-Ife, Nigeria.
cimoru@oauife.edu.ng
asheikh@oauife.edu.ng


Abstract:

In this paper, we obtain an integral inequality which extends Shum's and Imoru's generalization of Hardy's Inequality. Our main tool is Imoru's adaptation of Jensen's Inequality for convex functions.



4: Paper Source PDF document

Paper's Title:

On a Method of Proving the Hyers-Ulam Stability of Functional Equations on Restricted Domains

Author(s):

Janusz Brzdęk

Department of Mathematics
 Pedagogical University Podchor
ąźych 2,
30-084 Krak
ów,
Poland
jbrzdek@ap.krakow.pl

Abstract:

We show that generalizations of some (classical) results on the Hyers-Ulam stability of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable



4: 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.



4: Paper Source PDF document

Paper's Title:

Approximation of an AQCQ-Functional Equation and its Applications

Author(s):

Choonkil Park and Jung Rye Lee

Department of Mathematics,
Research Institute for Natural Sciences,
Hanyang University, Seoul 133-791,
Korea;

Department of Mathematics,
Daejin University,
Kyeonggi 487-711,
Korea

baak@hanyang.ac.kr
jrlee@daejin.ac.kr

Abstract:

This paper is a survey on the generalized Hyers-Ulam stability of an AQCQ-functional equation in several spaces. Its content is divided into the following sections:

1. Introduction and preliminaries.

2. Generalized Hyers-Ulam stability of an AQCQ-functional equation in Banach spaces: direct method.

3. Generalized Hyers-Ulam stability of an AQCQ-functional equation in Banach spaces: fixed point method.

4. Generalized Hyers-Ulam stability of an AQCQ-functional equation in random Banach spaces: direct method.

5. Generalized Hyers-Ulam stability of an AQCQ-functional equation in random Banach spaces: fixed point method.

6. Generalized Hyers-Ulam stability of an AQCQ-functional equation in non-Archi-medean Banach spaces: direct method.

7. Generalized Hyers-Ulam stability of an AQCQ-functional equation in non-Archi-medean Banach spaces: fixed point method.



4: 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.



4: 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.



3: Paper Source PDF document

Paper's Title:

Fixed Points and Stability of the Cauchy Functional Equation

Author(s):

Choonkil Park and Themistocles M. Rassias

Department of Mathematics, Hanyang University,
Seoul 133-791,
Republic of Korea

Department of Mathematics, National Technical University of Athens,
Zografou Campus, 15780 Athens,
Greece

baak@hanyang.ac.kr
trassias@math.ntua.gr

Abstract:

Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the Cauchy functional equation.



3: Paper Source PDF document

Paper's Title:

Stability Problems for Generalized Additive Mappings and Euler-Lagrange Type Mappings

Author(s):

M. Todoroki, K. Kumahara, T. Miura and S.-E. Takahasi

The Open University of Japan,
Chiba, 261-8586,
Japan
tomamiyu3232@sky.sannet.ne.jp
kumahara@ouj.ac.jp


 Yamagata University,
Yonezawa 992-8510,
Japan
miura@yz.yamagata-u.ac.jp

Toho University, Yamagata University,
Chiba, 273-0866,
Japan
sin_ei1@yahoo.co.jp

Abstract:

We introduce a generalized additivity of a mapping between Banach spaces and establish the Ulam type stability problem for a generalized additive mapping. The obtained results are somewhat different from the Ulam type stability result of Euler-Lagrange type mappings obtained by H. -M. Kim, K. -W. Jun and J. M. Rassias.



3: 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.



2: Paper Source PDF document

Paper's Title:

Applications of Relations and Relators in the Extensions of Stability Theorems for Homogeneous and Additive Functions

Author(s):

Árpád Száz

Institute of Mathematics, University of Debrecen,
H-4010 Debrecen, Pf. 12,
Hungary
szaz@math.klte.hu

Abstract:

By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Găvruţă in terms of the existence and unicity of 2-homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vector relator spaces. Thus, we obtain generalizations not only of the selection theorems of Z. Gajda and R. Ger, but also those of the present author.



2: 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.



2: Paper Source PDF document

Paper's Title:

Good and Special Weakly Picard Operators for the Stancu Operators with Modified Coefficients

Author(s):

Loredana-Florentina Galea and Alexandru-Mihai Bica

The Agora University of Oradea,
Piata Tineretului no. 8,
410526, Oradea,
Romania

University of Oradea,
Str. Universitatii No. 1,
410087, Oradea,
Romania

loredana.galea@univagora.ro
smbica@yahoo.com
abica@uoradea.ro


 

Abstract:

In this paper some properties of good and special weakly Picard operators for the Stancu operators with modified coefficients are obtained. In the study of the sequence of iterates of these operators, we obtain the property of dual monotone iteration.



2: 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.



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:

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.



1: Paper Source PDF document

Paper's Title:

Asymptotic Behavior of Mixed Type Functional Equations

Author(s):

J. M. 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 1983 Skof [24] was the first author to solve the Ulam problem for additive mappings on a restricted domain. In 1998 Jung [14] investigated the Hyers-Ulam stability of additive and quadratic mappings on restricted domains. In this paper we improve the bounds and thus the results obtained by Jung [14], in 1998 and by the author [21], in 2002. Besides we establish new theorems about the Ulam stability of mixed type functional equations on restricted domains. Finally, we apply our recent results to the asymptotic behavior of functional equations of different types.



1: Paper Source PDF document

Paper's Title:

On the Ulam Stability for Euler-Lagrange Type Quadratic Functional Equations

Author(s):

Matina John Rassias and John Michael Rassias

Statistics and Modelling Science,
University of Strathclyde,
Livingstone Tower,
26 Richmond Str,
Glasgow, Uk, G1 1xh

Pedagogical Department, E. E., National and Capodistrian University of Athens,
Section of Mathematics and Informatics,
4, Agamemnonos Str, Aghia Paraskevi,
Athens 15342, Greece
 

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 1992-2000 J.M. Rassias investigated the Ulam stability for Euler-Lagrange mappings. In this article we solve the Ulam problem for Euler-Lagrange type quadratic functional equations. These stability results can be applied in mathematical statistics, stochastic analysis, algebra, geometry, as well as in psychology and sociology.



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Paper's Title:

A general theory of decision making

Author(s):

Frank Hansen

Department of Economics,
University of Copenhagen,
Studiestraede 6, DK-1455 Copenhagen K
Denmark Frank.Hansen@econ.ku.dk
URL: http://www.econ.ku.dk/okofh


Abstract:

We formulate a general theory of decision making based on a lattice of observable events, and we exhibit a large class of representations called the general model. Some of the representations are equivalent to the so called standard model in which observable events are modelled by an algebra of measurable subsets of a state space, while others are not compatible with such a description. We show that the general model collapses to the standard model, if and only if an additional axiom is satisfied. We argue that this axiom is not very natural and thus assert that the standard model may not be general enough to model all relevant phenomena in economics. Using the general model we are (as opposed to Schmeidler [16]) able to rationalize Ellsberg's paradox without the introduction of non-additive measures.



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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.



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Paper's Title:

On Positive Entire Solutions of Second Order Quasilinear Elliptic Equations

Author(s):

Zuodong Yang and Honghui Yin

Institute of Mathematics, School of Mathematics and Computer Science,
Nanjing Normal University, Jiangsu Nanjing 210097,
China;
zdyang_jin@263.net

Department of Mathematics, Huaiyin Teachers College,
Jiangsu Huaian 223001,
China;
School of Mathematics and Computer Sciences,
Nanjing Normal University, Jiangsu Nanjing 210097,
China.
yin_hh@sina.com


Abstract:

In this paper, our main purpose is to establish the existence theorem of positive entire solutions of second order quasilinear elliptic equations under new conditions. The main results of the present paper are new and extend the previously known results.



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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.



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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.



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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.



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Paper's Title:

Strongly Nonlinear Variational Parabolic Problems in Weighted Sobolev Spaces

Author(s):

L. Aharouch, E. Azroul and M. Rhoudaf

Dép. Math. Faculté des Sciences Dhar-Mahraz
B.P 1796 Atlas Fés,
Maroc.
rhoudaf_mohamed@yahoo.fr 

Abstract:

In this paper , we study the existence of a weak solutions for the initial-boundary value problems of the strongly nonlinear degenerated parabolic equation,

∂u +A(u)+g(x,t,u,∇ u)=f
∂t

where A is a Leray-lions operator acted from Lp(0,T,W01,p(Ώ,w)) into its dual. g(x,t,u,∇ u) is a nonlinear term with critical growth condition with respect to ∇ u and no growth with respect to u. The source term f is assumed to belong to Lp'(0,T,W-1,p'(Ώ,w*)).



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Paper's Title:

A Fixed Point Approach to the Stability of the Equation

Author(s):

Soon-Mo Jung

Mathematics Section, College of Science and Technology
 Hong-Ik University, 339-701 Chochiwon
 Republic of Korea.

smjung@hongik.ac.kr

Abstract:

We will apply a fixed point method for proving the Hyers--Ulam stability of the functional equation .



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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



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Paper's Title:

Some Remarks on a Result of Bougoffa

Author(s):

James A. Oguntuase, Lars-Erik Persson and Josip E. Pečarič

Department of Mathematics,University of Agriculture,
 P M B 2240, Abeokuta, Nigeria

Department of Mathematics, Luleå University of Technology,
SE-971 87, Luleå , Sweden

Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb, Croatia
 
oguntuase@yahoo.com, larserik@sm.luth.se, pecaric@hazu.hr.

 

Abstract:

Some new generalizations of the result of L. Bougoffa [J. Inequal. Pure Appl. Math. 7 (2) (2006), Art. 60] are derived and discussed.
 



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Paper's Title:

An Lp Inequality for `Self-Reciprocal' Polynomials. II

Author(s):

M. A. Qazi

Department of Mathematics,
Tuskegee University,
Tuskegee, Alabama 36088
U.S.A.

qazima@aol.com

 

Abstract:

The main result of this paper is a sharp integral mean inequality for the derivative of a `self-reciprocal' polynomial.



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Paper's Title:

Ulam Stability of Reciprocal Difference and Adjoint Functional Equations

Author(s):

K. Ravi, J. M. Rassias and B. V. Senthil Kumar

Department of Mathematics,
Sacred Heart College, Tirupattur - 635601,
India

Pedagogical Department E. E.,
Section of Mathematics and Informatics,
National and Capodistrian University of Athens,
4, Agamemnonos Str., Aghia Paraskevi,
Athens, Attikis 15342,
GREECE

Department of Mathematics,
C.Abdul Hakeem College of Engineering and
Technology, Melvisharam - 632 509, India


shckavi@yahoo.co.in
jrassias@primedu.uoa.gr
bvssree@yahoo.co.in
 

Abstract:

In this paper, the reciprocal difference functional equation (or RDF equation) and the reciprocal adjoint functional equation (or RAF equation) are introduced. Then the pertinent Ulam stability problem for these functional equations is solved, together with the extended Ulam (or Rassias) stability problem and the generalized Ulam (or Ulam-Gavruta-Rassias) stability problem for the same equations.



1: 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.



1: 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



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Paper's Title:

Bilinear Regular Operators on Quasi-Normed Functional Spaces

Author(s):

D. L. Fernandez and E. B. Silva

Universidade Estadual de Campinas - Unicamp
Instituto de Matematica
Campinas - SP
Brazil.
E-mail: dicesar@ime.unicamp.br

Universidade Estadual de Maringa--UEM
Departamento de Matematica
Av.~Colombo 5790
Maringa - PR
Brazil.
E-mail: ebsilva@uem.br

Abstract:

Positive and regular bilinear operators on quasi-normed functional spaces are introduced and theorems characterizing compactness of these operators are proved. Relations between bilinear operators and their adjoints in normed functional spaces are also studied.



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Paper's Title:

Extreme Curvature of Polynomials and Level Sets

Author(s):

Stephanie P. Edwards, arah J. Jensen, Edward Niedermeyer, and Lindsay Willett

Department of Mathematics,
Hope College,
Holland, MI 49423,
U.S.A.
E-mail: sedwards@hope.edu
E-mail: tarahjaye@gmail.com
E-mail: eddie.niedermeyer@gmail.com
E-mail: willettlm1@gmail.com
WWW: http://math.hope.edu/sedwards/

Abstract:

Let f be a real polynomial of degree n. Determining the maximum number of zeros of kappa, the curvature of f, is an easy problem: since the zeros of kappa are the zeros of f'', the curvature of f is 0 at most n-2 times. A much more intriguing problem is to determine the maximum number of relative extreme values for the function kappa. Since kappa'=0 at each extreme point of kappa, we are interested in the maximum number of zeros of kappa'. In 2004, the first author and R. Gordon showed that if all the zeros of f'' are real, then f has at most n-1 points of extreme curvature. We use level curves and auxiliary functions to study the zeros of the derivatives of these functions. We provide a partial solution to this problem, showing that f has at most n-1 points of extreme curvature, given certain geometrical conditions. The conjecture that f has at most n-1 points of extreme curvature remains open.



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Paper's Title:

A Note on Calderon Operator

Author(s):

Chunping Xie

Department of Mathematics,
Milwaukee School of Engineering,
1025 N. Broadway,
Milwaukee, Wisconsin 53202,
U. S. A
.

E-mail: xie@msoe.edu

URL: http://www.msoe.edu/people/chunping.xie

Abstract:

We have shown that the Calderon operator is bounded on Morrey Spaces on R+. Also under certain conditions on the weight, the Hardy operator, the adjoint Hardy operator, and therefore the Caldern operator are bounded on the weighted Morrey spaces.



1: 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.



1: Paper Source PDF document

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.



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Paper's Title:

Residual-Based A Posteriori Error Estimates For A Conforming Mixed Finite Element Discretization of the Monge-Ampere Equation

Author(s):

J. Adetola, K. W. Houedanou and B. Ahounou

Institut de Mathematiques et de Sciences Physiques (IMSP),
Universite d'Abomey-Calavi
E-mail:  adetolajamal58@yahoo.com

Departement de Mathematiques,
Faculte des Sciences et Techniques (FAST),
Universite d'Abomey-Calavi
E-mail: khouedanou@yahoo.fr

Departement de Mathematiques,
Faculte des Sciences et Techniques (FAST),
Universite d'Abomey-Calavi
E-mail: bahounou@yahoo.fr

 

Abstract:

In this paper we develop a new a posteriori error analysis for the Monge-Ampere equation approximated by conforming finite element method on isotropic meshes in R2. The approach utilizes a slight variant of the mixed discretization proposed by Gerard Awanou and Hengguang Li in [4]. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.


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