Research article

Moroccan Journal of Pure and Applied Analysis

, 2:2

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Generalization of Some Inequalities for Differentiable Co-ordinated 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 co-ordinated convex, co-ordinated wright-convex and co-ordinated quasi-convex functions on the rectangle from the plane are established which provide weighted generalization of some recent results proved for co-ordinated 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

Hermite-Hadamard’s inequality co-ordinated convex function coordinated wright-convex function co-ordinated quasi-convex function Hölder’s integral inequality quadrature formula