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8: Paper Source PDF document

Paper's Title:

On an Extension of Hilbert’s Integral Inequality with Some Parameters

Author(s):

Bicheng Yang

Department of Mathematics, Guangdong Education College, Guangzhou, Guangdong 510303, People’s Republic of China.
bcyang@pub.guangzhou.gd.cn

URL
:
http://www1.gdei.edu.cn/yangbicheng/index.html

Abstract:

In this paper, by introducing some parameters and estimating the weight function, we give an extension of Hilbert’s integral inequality with a best constant factor. As applications, we consider the equivalent form and some particular results.



6: Paper Source PDF document

Paper's Title:

On a Hilbert-type Inequality with the Polygamma Function

Author(s):

Bing He and Bicheng Yang
Department of Mathematics, Guangdong Education College,
Guangzhou, 510303,
 China.

hzs314@163.com

Department of Mathematics, Guangdong Education College,
Guangzhou, 510303,
 China.

bcyang@pub.guangzhou.gd.cn

 

Abstract:

By applying the method of weight function and the technique of real analysis, a Hilbert-type inequality with a best constant factor is established, where the best constant factor is made of the polygamma function. Furthermore, the inverse form is given.



6: Paper Source PDF document

Paper's Title:

Stability of an Almost Surjective epsilon-Isometry in The Dual of Real Banach Spaces

Author(s):

Minanur Rohman, Ratno Bagus Edy Wibowo, Marjono

Department of Mathematics, Faculty of Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
E-mail: miminanira@gmail.com

Department of Mathematics, Faculty of Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
E-mail: rbagus@ub.ac.id

Department of Mathematics, Faculty of Mathematics and Natural Sciences,
Brawijaya University,
Jl. Veteran Malang 65145,
Indonesia.
E-mail: marjono@ub.ac.id

Abstract:

In this paper, we study the stability of epsilon-isometry in the dual of real Banach spaces. We prove that the almost surjective epsilon-isometry mapping is stable in dual of each spaces. The proof uses Gâteaux differentiability space (GDS), weak-star exposed points, norm-attaining operator, and some studies about epsilon-isometry that have been done before.



5: Paper Source PDF document

Paper's Title:

Oscillations of First Order Linear Delay Difference Equations

Author(s):

G. E. Chatzarakis and I. P. Stavroulakis

Department of Mathematics, University of Ioannina,
451 10, Greece
ipstav@cc.uoi.gr


Abstract:

Consider the first order linear delay difference equation of the form   where  is a sequence of nonnegative real numbers, k is a positive integer and  denotes the forward difference operator  New oscillation criteria are established when the well-known oscillation conditions  and  are not satisfied. The results obtained essentially improve known results in the literature.



4: Paper Source PDF document

Paper's Title:

The Invariant Subspace Problem for Linear Relations on Hilbert Spaces

Author(s):

Daniel Grixti-Cheng

Department of Mathematics and Statistics,
The University of Melbourne,
Melbourne, VIC, 3010
Australia.
D.Grixti@ms.unimelb.edu.au


Abstract:

We consider the invariant subspace problem for linear relations on Hilbert spaces with the aim of promoting interest in the problem as viewed from the theory of linear relations. We present an equivalence between the single valued and multivalued invariant subspace problems and give some new theorems pertaining to the invariant subspace problem for linear relations on a Hilbert space.



3: Paper Source PDF document

Paper's Title:

Two Mappings Related to Steffensen's Inequalities

Author(s):

Liang-Cheng Wang

School of Mathematical Science,
Chongqing Institute of Technology,
Xingsheng Lu 4,
Yangjiaping 400050, Chongqing City,
China.
wangliangcheng@163.com


Abstract:

In this paper, we define two mappings closely connected with Steffensen's inequalities, investigate their main properties, give some refinements for Steffensen's inequalities and obtain new inequalities.



3: Paper Source PDF document

Paper's Title:

A New Hardy-Hilbert's Type Inequality for Double Series and its Applications

Author(s):

Mingzhe Gao

Department of Mathematics and Computer Science, Normal College Jishou University,
Jishou Hunan, 416000,
People's Republic of China
mingzhegao1940@yahoo.com.cn


Abstract:

In this paper, it is shown that a new Hardy-Hilbert’s type inequality for double series can be established by introducing a parameter and the weight function of the form where c is Euler constant and And the coefficient is proved to be the best possible. And as the mathematics aesthetics, several important constants and appear simultaneously in the coefficient and the weight function when In particular, for case some new Hilbert’s type inequalities are obtained. As applications, some extensions of Hardy-Littlewood’s inequality are given.



2: Paper Source PDF document

Paper's Title:

Inequalities Relating to the Gamma Function

Author(s):

Chao-Ping Chen and Feng Qi

Department of Applied Mathematics and Informatics, Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo City, Henan 454000, China

chenchaoping@hpu.edu.cn

Department of Applied Mathematics and Informatics, Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo City, Henan 454000, China

qifeng@hpu.edu.cn, fengqi618@member.ams.org

U
rl: http://rgmia.vu.edu.au/qi.html, http://dami.hpu.edu.cn/qifeng.html

Abstract:

For , we have

                                     .

For,

                                    ,

 

 

And equality occurs for x=1.



2: Paper Source PDF document

Paper's Title:

Positive Periodic Time-Scale Solutions for Functional Dynamic Equations

Author(s):

Douglas R. Anderson and Joan Hoffacker

Department of Mathematics and Computer Science
Concordia College
Moorhead, MN 56562 USA
andersod@cord.edu
URL:
http://www.cord.edu/faculty/andersod/

Department of Mathematical Sciences
Clemson University
Clemson, SC 29634 USA
johoff@clemson.edu
URL:
http://www.math.clemson.edu/facstaff/johoff.htm


Abstract:

Using Krasnoselskii's fixed point theorem, we establish the existence of positive periodic solutions to two pairs of related nonautonomous functional delta dynamic equations on periodic time scales, and then extend the discussion to higher-dimensional equations. Two pairs of corresponding nabla equations are also provided in an analogous manner.



2: Paper Source PDF document

Paper's Title:

A Strengthened Hardy-Hilbert's Type Inequality

Author(s):

Weihong Wang and Bicheng Yang

Department of Mathematics, Guangdong Education Institute,
Guangzhou, Guangdong 520303,
People's Republic Of China
wwh@gdei.edu.cn
bcyang@pub.guangzhou.gd.cn
URL: http://www1.gdei.edu.cn/yangbicheng/index.html


Abstract:

By using the improved Euler-Maclaurin's summation formula and estimating the weight coefficient, we give a new strengthened version of the more accurate Hardy-Hilbert's type inequality. As applications, a strengthened version of the equivalent form is considered.



2: Paper Source PDF document

Paper's Title:

Local and Global Existence and Uniqueness Results for Second and Higher Order Impulsive Functional Differential Equations with Infinite Delay

Author(s):

Johnny Henderson and Abdelghani Ouahab

Department of Mathematics, Baylor University,
Waco, Texas 76798-7328
USA.
Johnny_Henderson@baylor.edu

Laboratoire de Mathématiques, Université de Sidi Bel Abbés
BP 89, 22000 Sidi Bel Abbées,
Algérie.
ouahab@univ-sba.dz


Abstract:

In this paper, we discuss the local and global existence and uniqueness results for second and higher order impulsive functional differential equations with infinite delay. We shall rely on a nonlinear alternative of Leray-Schauder. For the global existence and uniqueness we apply a recent Frigon and Granas nonlinear alternative of Leray-Schauder type in Fréchet spaces.



2: 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.



2: Paper Source PDF document

Paper's Title:

Existence of Positive Solutions for Nonlinear Fractional Differential Equations with Multi-point Boundary Conditions

Author(s):

N. Adjeroud

Khenchela University, Department of Mathematics,
Khenchela, 40000,
Algeria.
E-mail: adjnac@gmail.com

Abstract:

This paper is devoted to the existence results of positive solutions for a nonlinear fractional differential equations with multi-point boundary conditions. By means of the Schauder fixed point theorem, some results on the existence are obtained.



2: Paper Source PDF document

Paper's Title:

Cubic Alternating Harmonic Number Sums

Author(s):

Anthony Sofo

Victoria University,
College of Engineering and Science,
Melbourne City,
Australia.
E-mail: Anthony.Sofo@vu.edu.au

Abstract:

We develop new closed form representations of sums of cubic alternating harmonic numbers and reciprocal binomial coefficients. We also identify a new integral representation for the ζ (4)  constant.



2: Paper Source PDF document

Paper's Title:

Fractional exp(-φ(ξ))- Expansion Method and its Application to Space--Time Nonlinear Fractional Equations

Author(s):

A. A. Moussa and L. A. Alhakim

Department of Management Information System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
E-mail: Alaamath81@gmail.com
URL: https://scholar.google.com/citations?user=ccztZdsAAAAJ&hl=ar

Department of Management Information System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
E-mail: Lama2736@gmail.com
URL: https://scholar.google.com/citations?user=OSiSh1AAAAAJ&hl=ar

Abstract:

In this paper, we mainly suggest a new method that depends on the fractional derivative proposed by Katugampola for solving nonlinear fractional partial differential equations. Using this method, we obtained numerous useful and surprising solutions for the space--time fractional nonlinear Whitham--Broer--Kaup equations and space--time fractional generalized nonlinear Hirota--Satsuma coupled KdV equations. The solutions obtained varied between hyperbolic, trigonometric, and rational functions, and we hope those interested in the real-life applications of the previous two equations will find this approach useful.



1: 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.



1: Paper Source PDF document

Paper's Title:

L∞- Error Estimate of Schwarz Algorithm for Elliptic Quasi-Variational Inequalities Related to Impulse Control Problem

Author(s):

Saadi Samira and Mehri Allaoua

Lab. LANOS, Department of Mathematics,
University Badji Mokhtar Annaba,
P.O.Box 12, Annaba 23000,
Algeria.

Lab. LAIG, Department of Mathematics,
University May 8th 1945,
P.O.Box 401, Guelma 24000,
Algeria.

E-mail: saadisamira69@yahoo.fr
allmehri@yahoo.fr

Abstract:

In this work, we study Schwarz method for a class of elliptic quasi-variational inequalities. The principal result of this investigation is to prove the error estimate in ∞-norm for two domains with overlapping nonmatching grids, using the geometrical convergence, and the uniform convergence of Cortey Dumont.



1: Paper Source PDF document

Paper's Title:

Credibility Based Fuzzy Entropy Measure

Author(s):

G. Yari, M. Rahimi, B. Moomivand and P. Kumar

Department of Mathematics,
Iran University of Science and Technology,
Tehran,
Iran.
E-mail: Yari@iust.ac.ir
E-mail: Mt_Rahimi@iust.ac.ir
URL: http://www.iust.ac.ir/find.php?item=30.11101.20484.en
URL: http://webpages.iust.ac.ir/mt_rahimi/en.html

Qarzol-hasaneh
Mehr Iran Bank, Tehran,
Iran.
E-mail: B.moomivand@qmb.ir

Department of Mathematics and Statistics,
University of Northern British Columbia,
Prince George, BC,
Canada.
E-mail: Pranesh.Kumar@unbc.ca

Abstract:

Fuzzy entropy is the entropy of a fuzzy variable, loosely representing the information of uncertainty. This paper, first examines both previous membership and credibility based entropy measures in fuzzy environment, and then suggests an extended credibility based measure which satisfies mostly in Du Luca and Termini axioms. Furthermore, using credibility and the proposed measure, the relative entropy is defined to measure uncertainty between fuzzy numbers. Finally we provide some properties of this Credibility based fuzzy entropy measure and to clarify, give some examples.



1: 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.



1: Paper Source PDF document

Paper's Title:

Some New Mappings Related to Weighted Mean Inequalities

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 four mappings related to weighted mean inequalities, investigate their properties, and obtain some new refinements of weighted mean inequalities.


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