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 (...

We propose the concept of up and down harmonically convex mapping for fuzzy-number-valued as our main goal in this work. With help fuzzy-number convexity fuzzy fractional integral operator, we also show results Hermite–Hadamard (H–H) inequality, Fejér type some other related versions inequalities. Moreover, examples are presented to discuss validity results. The from new technique how suggested...

Results involving the approximation of the difference between two integral means are utilised to obtain bounds on the Integral Mean Divergence and the f−divergence due to Csiszár. The current work does not restrict the functions involved to be convex. If convexity is imposed then the Integral Mean Divergence is the Hermite-Hadamard divergence introduced by Shioya and Da-te.

In the paper, the authors establish some integral inequalities of Hermite-Hadamard type for co-ordinated (α1,m1)-(α2,m2)convex functions on a rectangle of the first quadrant in a plane.

In the paper, the authors introduce a new notion "[Formula: see text]-convex function on the co-ordinates" and establish some Hermite-Hadamard type integral inequalities for [Formula: see text]-convex functions on the co-ordinates.

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...