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.
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2010 Mathematics Subject Classification. 26D15, 26A45, 26D10, 41A55.
a School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa.
e-mail: m amer latif@hotmail.com, ebrahim.momoniat@wits.ac.za.
b School of Engineering and Science, Victoria University, PO Box 14428 Melbourne City, MC 8001, Australia.
e-mail: sever.dragomir@vu.edu.au.
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Latif, M., Dragomir, S. & Momoniat, E. Generalization of Some Inequalities for Differentiable Co-ordinated Convex Functions With Applications. Moroc J Pure Appl Anal 2, 2 (2016). https://doi.org/10.7603/s40956-016-0002-4
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DOI: https://doi.org/10.7603/s40956-016-0002-4