Hermite–Hadamard and Jensen‐Type Inequalities via Riemann Integral Operator for a Generalized Class of Godunova–Levin Functions

Abstract

The generalization of Godunova–Levin interval-valued functions has been drastically studied in last few decades, as it has a remarkable applications in both pure and applied mathematics. The goal of this study is to introduce the notion of h-Godunova–Levin interval-valued functions. We establish Hermite–Hadamard and Jensen-type inequalities via Riemann integral operator.

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

“…Proof. If ℵ satisfies (7), then (4) holds with ‫ג‬ = ℵ + ϵ. Therefore, by virtue of Corollary 1, there exists a two-variable convex function h :…”

“…Following are some recently introduced classes of generalized convex mappings: p-convex, harmonic convex, exponentially convex, Godunova-Levin, preinvexity, (h 1 , h 2 )-convex, coordinated convex, log-convex, and many more (see refs. [7][8][9]). The Hermite-Hadamard inequality has been interpreted in various ways by different authors by using these novel classes.…”

Hermite–Hadamard-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Godunova–Levin and (h1, h2)-Convex Functions

“…As a result of studying the Strong literature and specific articles [12,39,40], we reformulated the above two results based on Caputo-Fabrizio fractional integral operators.…”

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

“…Further, here are some practical applications of interval analysis in various linear and nonlinear disciplines, see Refs. [4,5]. As we know, Hermite-Hadamard inequality is the first geometric interpretation of a convex function and it is widely used in several disciplines that involve convex optimization.…”