Some Fejér type inequalities for strongly (Mϕ,Mψ) - convex functions
Abstract
In this paper, we propose and study a class of generalized convex functions, which are defined according to a pair of quasi-arithmetic means and called (Mϕ,Mψ)-convex functions, and establish various Fejér type inequalities for such a function class. These inequalities not merely provide a natural and intrinsic characterization of the (Mϕ,Mψ)-convex functions, but actually offer a generalizarion and refinement of some Hermite-Hadamard and Fejér type inequalities obtained in earlier studies for different kinds of strong convexity.