Refinement of Jensen Mercer and Hermite–Hadamard-Mercer type inequalities for generalized convex functions on co-ordinates with their computational analysis

Muhammad Toseef, Zhiyue Zhang*, Abdul Mateen, Hüseyin Budak and Artion Kashuri

In the current study, the Jensen-Mercer inequality is extended to co-ordinated h-convex functions. Additionally, a novel inequality is employed to derive Hermite–Hadamard-Mercer type inequalities for h-convex functions defined on the co-ordinates of a rectangle in the plane. These developments not only reinforce the core tenets of convex analysis but also expand the applicability of Hermite-Hadamard-Mercer type inequalities to generalized convex functions on co-ordinates. This provides valuable tools for data analysis and optimization problem-solving. The practical utility and efficacy of this generalized inequality in real-world scenarios involving co-ordinates are demonstrated through a computational study.

Mathematics Subject Classification: 26D10, 26D15, 26A51, 34A08.

Keywords:

Published on: Jun 28, 2024 Pages: 190-205

Full Text PDF Full Text HTML DOI: 10.17352/amp.000123
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