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

Abstract

Motivated by some recently established  Jensen-type operator inequalities related to a   convex function, in the present paper we derive several more accurate  Jensen-type operator inequalities for certain subclasses of convex functions. More precisely, we obtain interpolating series of Jensen-type inequalities utilizing  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.