Operator inequalities for h-convex functions with applications

In this paper, we generalize the operator version of Jensen's inequality and the converse one for the class of h -convex functions.We extend the Hermite-Hadamard's type inequality and a multiple operator version of Jensen's inequality for this class of functions.We also provide a refinement of Jensen's inequality for convex functions.In particular, the operator hconvexity can be reduced to usual h -convexity in some sense and some results for the other classes of functions can be deduced by choosing an appropriate function h .The superiority of our results is that our results can recover some known results.