Fuzzy Hermite-Hadamard type inequality for r-preinvex and ({\alpha},m)-preinvex function

TL;DR

This paper extends Hermite-Hadamard inequalities to r-preinvex and ({\alpha},m)-preinvex functions using Sugeno integrals, broadening the scope of convexity-based inequalities.

Contribution

It introduces new Hermite-Hadamard type inequalities for r-preinvex and ({\alpha},m)-preinvex functions via Sugeno integrals, expanding existing theoretical frameworks.

Findings

Derived new inequalities for r-preinvex functions

Extended Hermite-Hadamard inequalities to ({\alpha},m)-preinvex functions

Provided theoretical bounds based on Sugeno integrals

Abstract

The purpose of this paper is to study the Hermite-Hadamard type inequality for r-preinvex and ({\alpha}, m)-preinvex function which is based on Sugeno integral.