Abstract The Hermite-Hadamard inequality is regarded as one of the most favorable inequalities from research point view. Currently, mathematicians are working on extending, improving, and generalizing this inequality. This article presents conticrete Hermite-Hadamard-Jensen-Mercer type in weighted unweighted forms by using idea majorization convexity together with generalized conformable fracti...

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...

Abstract There are a lot of papers dealing with applications the so-called cyclic refinement discrete Jensen’s inequality. A significant generalization refinement, based on combinatorial considerations, has recently been discovered by author. In present paper we give integral versions these results. On one hand, new method to refine inequality is developed. other result contains some recent ref...

The aim of the present paper is to extend the classical Hermite-Hadamard inequality to the case when the convexity notion is induced by a Chebyshev system.

The left Hermite-Hadamard inequality of several variables for convex functions on certain convex compact sets is proved via elementary approach, independently of Choquet theory.

In this paper we introduce the concept of geometrically quasiconvex functions on the co-ordinates and establish some Hermite-Hadamard type integral inequalities for functions defined on rectangles in the plane. Some  inequalities for product of two geometrically quasiconvex functions on the co-ordinates are considered.

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

In this paper we prove some inequalities for convex function of a higher order. The well known Hermite interpolating polynomial leads us to a converse of Jensen inequality for a regular, signed measure and, as a consequence, a generalization of Hadamard and Petrovi c's inequalities. Also, we obtain a new upper bound for the error function of the Hermite interpolating polynomial je H (x)j in ter...

Abstract In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion $q^{b}$ qb -integral. We prove some new related with right-hand sides -Hermite–Hadamard for differentiable absolute values second derivatives. The results present...

Abstract In this paper, we explore a class of Hermite–Hadamard integral inequalities for convex and m -convex functions. The Hölder inequality is used to create class, which has wide range applications in optimization theory. Some trapezoid-type midpoint error estimates are investigated. Inequalities several q -special functions highlighted. As particular cases, have included previous results.