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We aim to establish certain generalized Hermite-Hadamard's inequalities for generalized convex functions via local fractional integral. As special cases of some of the results presented here, certain interesting inequalities involving generalized arithmetic and logarithmic means are obtained.

Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named $(k,s)$ -Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

In this paper, we introduce some new concepts to the field of probability theory: \(\left( k,s\right) \)-Riemann–Liouville fractional expectation and variance functions. Some generalized integral inequalities are established for \(\left( k,s\right) \)-Riemann–Liouville expectation and variance functions.

We aim to present some new Pólya-Szegö type inequalities associated with Hadamard k-fractional integral operators, which are also used to derive some Chebyshev type integral inequalities. Further we apply some of the results presented here to a function which is bounded by the Heaviside functions.

In this study, s-convex stochastic processes in the second sense are presented and some well-known results concerning s-convex functions are extended to s-convex stochastic processes in the second sense. Also, we investigate relation between s-convex stochastic processes in the second sense and convex stochastic processes.

In this paper, we aim to present the improved version of the reverse Holder type inequalities by taking \((k,s)-\)Riemann-Liouville fractional integrals. Furthermore, we also discuss some applications of Theorem 1 using some types of fractional integrals.

Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(k,s)$\end{document}(k,s)-Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

In this paper, we consider the class of generalized quasi-convex. Then using this convexity, we obtain some new generalized Hermite-Hadamard type integral inequalities for the generalized quasi-convex functions.

International Conference on Advances in Natural and Applied Sciences (ICANAS) -- APR 21-23, 2016 -- Antalya, TURKEY SET, ERHAN/0000-0003-1364-5396 WOS: 000376001000035 In this paper, we prove a useful lemma. After that, using this lemma, we obtain several new Hermite-Hadamard type of inequalities for Reimann-Liouville fractional integrals.

SET, ERHAN/0000-0003-1364-5396 WOS: 000361771500005 The aim of the present paper is to investigate some new integral inequalities of Gruss type for k - Riemann-Liouville fractional integrals. From our results, new weighted or classical Griiss type inequalities have been established for some special cases. Moreover, special cases of the integral inequalities in this paper have been obtained by Dahmani and Tabharit, 2010 in [5]. (C) 2015 Elsevier Inc. All rights reserved.