Generalized Preinvex Interval-Valued Functions and Related Hermite–Hadamard Type Inequalities

Abstract

This study aims to connect the idea of inequalities with Riemann integral operators, which are of interest because of their characteristics and widespread use. We create a new Hermite–Hadamard type integral inequality for an 𝔴-preinvex interval-valued function using an interval integral operator. In the context of pseudo-order relations, we also establish new variations of the Fejér type inequalities and the Pachpatte type inequalities. We further verify the veracity of the conclusions we draw in this study by providing a number of numerical examples. The findings given in this work, in our opinion, are innovative and will help spur more study in this area.

Keywords

• Hermite–Hadamard inequalities
• interval-valued functions
• Riemann integral operator