In this paper we establish new Hermite-Hadamard type inequalities involving fractional integrals with respect to another function. Such fractional integrals generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. c ©2016 All rights reserved.

In this paper, the author introduced the concept of generalized harmonically convex function on fractal sets Rα(0 < α 6 1) of real line numbers and established generalized Hermite-Hadamard’s inequalities for generalized harmonically convex function. Then, by creating a local fractional integral identity, obtained some Hermite-Hadamard type inequalities of these classes of functions. c ©2017 All...

In this paper, we present some new refinements of Hermite–Hadamard inequalities for continuous convex functions by using (p,q)-calculus. Moreover, study (p,q)-Hermite–Hadamard multiple integrals. Many results given in paper provide extensions others previous research.

We firstly give a modification of the known Hermite-Hadamard type inequalities for the generalized k-fractional integral operators of a function with respect to another function. We secondly establish several Hermite-Hadamard type inequalities for the generalized k-fractional integral operators of a function with respect to another function. The results presented here, being very general, are p...

This article deals with the different classes of convexity and generalizations. Firstly, we reveal the new generalization of the definition of convexity that can reduce many order of convexity. We have showed features of algebra for this new convex function. Then after we have constituted Hermite-Hadamard type inequalities for this class of functions. Finally the identity has been revealed for ...

Some generalizations and refinements of Hermite-Hadamard type inequalities related to [Formula: see text]-convex functions are investigated. Also applications for trapezoid and mid-point type inequalities are given.

By Hölder's integral inequality, the authors establish some Hermite-Hadamard type integral inequalities for n-times differentiable and geometrically quasi-convex functions.

In this paper, some Hermite-Hadamard-Fejer type integral inequalities for harmonically s-convex functions in fractional integral forms have been obtained.

The author introduces the concept of harmonically convex functions and establishes some Hermite-Hadamard type inequalities of these classes of functions.

Abstract Under the new concept of s - $(\alpha,m)$ ( α , m ) -convex functions, we obtain some Hermite–Hadamard inequalities with an function. We use these to estimate Riemann–Liouville fractional integrals second-order differentiable convex ...