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arXiv · 1604.03358

New Hermite-Hadamard Type Inequalities for Twice Differentiable Composite $(h-s)_2$-Convex Functions

Peter Olamide Olanipekun·Adesanmi Alao Mogbademu
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Abstract

In a recent paper [9], Ozdemir, Tunc and Akdemir defined two new classes of convex functions with which they proved some Hermite-Hadamard type inequalities. As an Open problem, they asked for conditions under which the composition of two functions belong to their newly defined class of convex functions and if Hermite-Hadamard type inequalities can be obtained. In this paper, we respond to the Open problems and prove some new Hermite-Hadamard inequalities for twice differentiable composition whose second derivative is $((h-s)_{2}, I)$-convex. Our results are applied to some special means of real numbers.

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Peter Olamide Olanipekun, Adesanmi Alao Mogbademu. 2016-04-12. New Hermite-Hadamard Type Inequalities for Twice Differentiable Composite $(h-s)_2$-Convex Functions. https://arxiv.org/abs/1604.03358

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