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arXiv · 2201.05862

Mond and Pe$\check{c}$ari$\acute{c}$ inequality for $h$-convex functions with applications

Ismail Nikoufar·Davuod Saeedi
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Abstract

In this paper, we prove an operator version of the Jensen's inequality and its converse for $h$-convex functions. We provide a refinement of the Jensen type inequality for $h$-convex functions. Moreover, we prove the Hermite-Hadamard's type inequality and a multiple operator version of the Jensen's inequality for $h$-convex functions. In particular, a result for convex, $P$-class, $s$-convex, Godunova-Levin, and $s$-Godunova-Levin functions can be deduced.

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Ismail Nikoufar, Davuod Saeedi. 2022-01-15. Mond and Pe$\check{c}$ari$\acute{c}$ inequality for $h$-convex functions with applications. https://arxiv.org/abs/2201.05862

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