Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr-h-Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings

Abstract

The application of fractional calculus to interval analysis is vital for the precise derivation of integral inequalities on set-valued mappings. The objective of this article is to reformulated the well-known Hermite–Hadamard inequality into various new variants via fractional integral operator (Riemann–Liouville ) and generalize the various previously published results on set-valued mappings via center and radius order relations using harmonical h-convex functions. First, using these notions, we developed the Hermite–Hadamard (H--H) inequality, and then constructed some product form of these inequalities for harmonically convex functions. Moreover, to demonstrate the correctness of these results, we constructed some interesting non-trivial examples.

Hyers–Ulam Stability of 2D-Convex Mappings and Some Related New Hermite–Hadamard, Pachpatte, and Fejér Type Integral Inequalities Using Novel Fractional Integral Operators via Totally Interval-Order Relations with Open Problem

“…We refer to these works for more recent developments about similar conclusions using various other kinds of convex mappings and integral operators (see Refs. [35][36][37][38][39][40]).…”

Weighted Fejér, Hermite–Hadamard, and Trapezium-Type Inequalities for (h1,h2)–Godunova–Levin Preinvex Function with Applications and Two Open Problems

“…The following are some features and uses of generalised convexity: log-convex, p-convex, h-convex, preinvexity, Godunova-Levin, exponentially convex, harmonic convex, and many others (see refs. [7][8][9][10][11][12][13]). As a result of these different classes, various authors developed the following double inequality for convex function in different perspectives, and it is the most crucial factor in optimization [14].…”