On the operator Acz\'{e}l inequality and its reverse

TL;DR

This paper explores new operator and eigenvalue inequalities related to the Aczél inequality and its reverse, utilizing operator monotone, doubly concave, and convex functions with the generalized Kantorovich constant.

Contribution

It introduces novel variants of the operator Aczél inequality and its reverse, expanding the theoretical framework with generalized constants and function classes.

Findings

New operator inequalities involving eigenvalues

Variants of Aczél inequality and reverse established

Use of generalized Kantorovich constant in inequalities

Abstract

In this paper, we present some operator and eigenvalue inequalities involving operator monotone, doubly concave and doubly convex functions. These inequalities provide some variants of operator Acz\'{e}l inequality and its reverse via generalized Kantorovich constant.