Operator Popoviciu's inequality for superquadratic and convex functions of selfadjoint operators in Hilbert spaces

TL;DR

This paper extends Popoviciu's inequality to positive selfadjoint operators in Hilbert spaces for superquadratic and convex functions, providing new operator inequalities and related results.

Contribution

It introduces operator versions of Popoviciu's inequality for superquadratic and convex functions in Hilbert spaces, a novel extension of classical inequalities.

Findings

Operator Popoviciu's inequality for superquadratic functions proved

Operator Popoviciu's inequality for convex functions established

Additional related inequalities derived

Abstract

In this work, operator version of Popoviciu's inequality for positive selfadjoint operators in Hilbert spaces under positive linear maps for superquadratic functions is proved. Analogously, using the same technique operator version of Popoviciu's inequality for convex functions is obtained. Some other related inequalities are also deduced.