Interpolating operator Jensen-type inequalities for log-convex and superquadratic functions

TL;DR

This paper develops refined operator Jensen-type inequalities for log-convex and superquadratic functions, providing more accurate bounds and interpolating series that improve upon existing inequalities.

Contribution

It introduces new interpolating series of Jensen-type inequalities for specific subclasses of convex functions, refining known operator inequalities.

Findings

Derived more accurate Jensen-type inequalities for log-convex functions.

Established refinements of Jensen-Mercer operator inequality.

Provided interpolating series that enhance existing bounds.

Abstract

Motivated by some recently established operator Jensen-type inequalities related to a usual convexity, in the present paper we derive several more accurate operator Jensen-type inequalities for certain subclasses of convex functions. More precisely, we obtain interpolating series of Jensen-type inequalities for log-convex and non-negative superquadratic functions. In particular, we obtain the corresponding refinements of the Jensen-Mercer operator inequality for such classes of functions.