Some Hermite-Hadamard type inequalities for the product of two operator preinvex functions

TL;DR

This paper introduces operator preinvex functions and establishes Hermite-Hadamard type inequalities for these functions, including bounds for the product of two such functions on selfadjoint operators in Hilbert spaces.

Contribution

It presents the concept of operator preinvex functions and derives new Hermite-Hadamard inequalities for them, extending existing inequalities to the operator setting.

Findings

Established Hermite-Hadamard inequalities for operator preinvex functions.

Provided bounds for the product of two operator preinvex functions.

Extended classical inequalities to the context of selfadjoint operators in Hilbert spaces.

Abstract

In this paper we introduce operator preinvex functions and es- tablish a Hermite-Hadamard type inequality for such functions. We give 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. Also some Hermite-Hadamard type inequalities for the product of two operator preinvex functions are given.