Ostrowski Type Inequalities Via ψ − (α, β, γ, δ)−Convex Function

Abstract

In this paper, we are introducing very first time the class of ψ − (α, β, γ, δ)−convex function in mixed kind, which is the generalization of many classes of convex functions. We would like to state well-known Ostrowski inequality via Montgomery identity for ψ−(α, β, γ, δ)−convex function in mixed kind. In addition, we establish some Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are ψ − (α, β, γ, δ)-convex functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means would also be given. Keywords: Ostrowski inequality, Montgomery identity, convex functions, special means.