ostrowski type inequalities via (α, β, γ, δ)-convex function

In this paper, we are introducing very first time the class of (α, β, γ, δ)− convex (concave) function in mixed kind, which is the generalization of many classes of functions given in [2, 3, 4, 15, 16, 17]. we would like to state the well-known ostrowski inequality via generalized montgomery identity [14] for (α, β, γ, δ)− convex (concave) 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 (α, β, γ, δ)-convex (concave) functions in mixed kind by using different techniques including hölder’s inequality [27] and power mean inequality [26]. also, various established results would be captured as special cases. moreover, some applications in terms of special means would also be given.