Some Hermite-Hadamard type inequalities for (P, m)-function and quasi m-convex functions

In this paper, we introduce a new class of functions called as (P, m)-function and quasi-m-convex function. Some inequalities of Hadamard's type for these functions are given. Some special cases are discussed. Results represent significant refinement and improvement of the previous results. We should especially mention that the definition of (P, m)-function and quasi-m-convexity are given for the first time in the literature and moreover, the results obtained in special cases coincide with the well-known results in the literature.