Hermite-Hadamard type inequalities for operator geometrically convex functions

TL;DR

This paper introduces operator geometrically convex functions and establishes Hermite-Hadamard type inequalities for them, leading to refined trace inequalities for positive linear operators.

Contribution

It defines operator geometrically convex functions and proves new Hermite-Hadamard inequalities, extending previous operator inequalities with applications to trace inequalities.

Findings

Established Hermite-Hadamard inequalities for operator geometrically convex functions.

Derived refined trace inequalities for positive linear operators.

Extended existing inequalities in operator theory.

Abstract

In this paper, we introduce the concept of operator geometrically convex functions for positive linear operators and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain trace inequalities for operators which give some refinements of previous results.