<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications

School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg,

School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa

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

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications

Article Category: Research Article

Published Online: Feb 04, 2017

Page range: 12 - 32

Received: Feb 16, 2016

Accepted: Mar 30, 2016

DOI: https://doi.org/10.7603/s40956-016-0002-4

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

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications

Article Category: Research Article

Published Online: Feb 04, 2017

Page range: 12 - 32

Received: Feb 16, 2016

Accepted: Mar 30, 2016

DOI: https://doi.org/10.7603/s40956-016-0002-4

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

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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