Moroccan Journal of Pure and Applied Analysis
, 2:2
First online:
Generalization of Some Inequalities for Differentiable Coordinated Convex Functions With Applications
 M. A. LatifAffiliated withSchool of Computational and Applied Mathematics, University of the Witwatersrand Email author
 , S. S. DragomirAffiliated withSchool of Computational and Applied Mathematics, University of the WitwatersrandSchool of Engineering and Science, Victoria University
 , E. MomoniatAffiliated withSchool of Computational and Applied Mathematics, University of the Witwatersrand
Abstract
In this paper, a new weighted identity for functions defined on a rectangle from the plane is established. By using the obtained identity and analysis, some new weighted integral inequalities for the classes of coordinated convex, coordinated wrightconvex and coordinated quasiconvex functions on the rectangle from the plane are established which provide weighted generalization of some recent results proved for coordinated convex functions. Some applications of our results to random variables and 2D weighted quadrature formula are given as well.
2000 Mathematics Subject Classification. 26D15, 26D20, 26D07.
Key words and phrases
HermiteHadamard’s inequality coordinated convex function coordinated wrightconvex function coordinated quasiconvex function Hölder’s integral inequality quadrature formula Title
 Generalization of Some Inequalities for Differentiable Coordinated Convex Functions With Applications
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Moroccan Journal of Pure and Applied Analysis
2:2
 Online Date
 April 2016
 DOI
 10.7603/s4095601600024
 Online ISSN
 23518227
 Publisher
 University Sidi Mohamed Ben Abdallah
 Additional Links
 Topics
 Keywords

 HermiteHadamard’s inequality
 coordinated convex function
 coordinated wrightconvex function
 coordinated quasiconvex function
 Hölder’s integral inequality
 quadrature formula
 Authors

 M. A. Latif ^{(1)}
 S. S. Dragomir ^{(1)} ^{(2)}
 E. Momoniat ^{(1)}
 Author Affiliations

 1. School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa
 2. School of Engineering and Science, Victoria University, 14428, MC 8001, Melbourne, Australia