hold. This double inequality is known in the literature as the Hermite–Hadamard inequality for convex functions. In recent years many authors established several inequalities connected to this fact. For recent results, refinements, counterparts, generalizations and new Hermite-Hadamard’stype inequalities see [1]–[18]. We recall that the notion of quasi-convex function generalizes the notion of ...

In the present work, we introduce two new local fractional integral operators involving Mittag–Leffler kernel on Yang’s fractal sets. Then, study related generalized Hermite–Hadamard-type inequality using (E,h)-convexity and obtain identities pertaining to these operators, respective first- second-order derivatives are given. terms of applications, provide some trapezoid-type inequalities for (...

Abstract In this paper, we obtain new Hermite–Hadamard-type inequalities for r -convex and geometrically convex functions and, additionally, some by using the Hölder–İşcan integral inequality an improved power-mean inequality.

Abstract In this paper, we introduce $(h_{1},h_{2})$ ( h 1 , 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex functions by using Riemann–Liouville fracti...