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arXiv · 1704.08190

Generalized Convex Functions and Their Applications

Adem Kilicman·Wedad Saleh
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Abstract

This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex functions and establish some their properties. Moreover, we give generalized $ s $-convex functions in the second sense and present some new inequalities of generalized Hermite-Hadamard type for the class of functions whose second local fractional derivatives of order $ \alpha $ in absolute value at certain powers are generalized $ s $-convex functions in the second sense. At the end, some examples that these inequalities are able to be applied to some special means are showed.

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Adem Kilicman, Wedad Saleh. 2017-04-15. Generalized Convex Functions and Their Applications. https://arxiv.org/abs/1704.08190

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