Operator inequalities associated with the Kantrovich type inequalities for $s$-convex functions

TL;DR

This paper extends Kantorovich type inequalities to operators involving s-convex functions, providing new bounds and applications in operator theory, including improved bounds for the numerical radius of positive operators.

Contribution

It introduces novel operator inequalities related to s-convex functions and applies them to derive bounds for the numerical radius and order-preserving inequalities.

Findings

Established new operator inequalities for s-convex functions.

Derived a better lower bound for the numerical radius of positive operators.

Applied inequalities to order-preserving power inequalities of three variables.

Abstract

In this paper, we prove some operator inequalities associated with an extension of the Kantorovich type inequality for $s$-convex function. We also give an application to the order preserving power inequality of three variables and find a better lower bound for the numerical radius of a positive operator under some conditions.