Some integral inequalities for operator arithmetic-geometrically convex functions

TL;DR

This paper introduces operator arithmetic-geometrically convex functions, establishes Hermite-Hadamard type inequalities, and derives trace and norm inequalities for positive linear operators, refining existing results in operator theory.

Contribution

It presents new definitions and inequalities for operator convex functions, extending classical inequalities to the operator setting with applications to trace and norm bounds.

Findings

Hermite-Hadamard type inequalities for operator convex functions

Refined trace inequalities for positive linear operators

Unitarily invariant norm inequalities for operators

Abstract

In this paper, we introduce the concept of operator arithmetic-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. Moreover, some unitarily invariant norm inequalities are established.