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

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