THE HERMITE-HADAMARD TYPE INEQUALITIES FOR OPERATOR m-CONVEX FUNCTIONS IN HILBERT SPACE

Abstract

− In this paper, we first define operators m-convex functions for positive, bounded, selfadjoint operators in Hilbert space via m-convex functions. Secondly, we establish some new theoremsfor them. Finally, we obtain the Hermite-Hadamard type inequalities for the product two operatorsm-convex functions in Hilbert space