Ostrowski type inequalities via (\alpha,\beta,\gamma,\delta)-convex function

In this paper, we are introducing very first time the class of (\alpha,\beta,\gamma,\delta)- convex (concave) function in mixed kind, which is the generalization of many classes of functions given in   [۲, ۳, ۴, ۱۵, ۱۶, ۱۷].  We would like to state the well-known Ostrowski inequality via generalized Montgomery identity [۱۴] for (\alpha,\beta,\gamma,\delta)- 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 (\alpha,\beta,\gamma,\delta)-convex (concave) functions in mixed kind by using different techniques including Holder's inequality [۲۷] and power mean inequality [۲۶]. 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 , Generalized Montgomery identity , Convex functions , special means