LAUSR

Abstract We consider a class of generalized convex functions, which are defined according to a pair of quasi-arithmetic means and called ( M ϕ , M ψ ) -convex functions, and establish various Fejer type inequalities for such a function class. These inequalities not merely provide a natural and intrinsic characterization of the ( M ϕ , M ψ ) -convex functions, but actually offer a generalization and refinement of the most part of the concrete Hermite-Hadamard and Fejer type inequalities obtained in earlier studies for different kinds of convexity and fractional integrals. Applications to inequalities involving the gamma function and special means are also included.