Hermite-Hadamard type inequality for operator preinvex functions

TL;DR

This paper extends Hermite-Hadamard inequalities to operator preinvex functions, providing new bounds for selfadjoint operators in Hilbert spaces, thus broadening the scope of convexity-based inequalities in operator theory.

Contribution

It introduces a Hermite-Hadamard type inequality specifically for operator preinvex functions, a novel class in the context of operator inequalities.

Findings

Established a Hermite-Hadamard inequality for operator preinvex functions.

Provided an estimate for the right-hand side of the inequality involving selfadjoint operators.

Extended classical inequalities to a new class of operator functions.

Abstract

In this paper we establish a Hermite- Hadamard type inequality for operator preinvex functions and an estimate of the right hand side of a Hermite- Hadamard type inequality in which some operator preinvex functions of selfadjoint operators in Hilbert spaces are involved.