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

Abstract

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