Pompeiu-Chebyshev type inequalities for selfadjoint operators in Hilbert spaces

TL;DR

This paper generalizes inequalities related to continuous $h$-synchronous and $h$-asynchronous functions of selfadjoint operators in Hilbert spaces, expanding the theoretical framework of operator inequalities.

Contribution

It introduces new generalized inequalities for selfadjoint operators based on $h$-synchronous and $h$-asynchronous functions, extending existing operator inequality theory.

Findings

New inequalities for selfadjoint operators proved

Generalizations applicable to various functions in Hilbert spaces

Theoretical advancement in operator inequality literature

Abstract

In this work, generalization of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved.