Mond and Pe\(\check{c}\)ari\(\acute{c}\) inequality for \(h\)-convex functions with applications

In this paper, we prove an operator version of the Jensen's inequality and its converse for \(h\)-convex functions. We provide a refinement of the Jensen type inequality for \(h\)-convex functions. Moreover, we prove the Hermite-Hadamard's type inequality and a multiple operator version of the Jensen's inequality for \(h\)-convex functions. In particular, a result for convex, \(P\)-class, \(s\)-convex, Godunova-Levin, and \(s\)-Godunova-Levin functions can be deduced.