فهرست نشریات علمی دسترسی آزاد ایران

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   [2, 3, 4, 15, 16, 17].  We would like to state the well-known Ostrowski inequality via generalized Montgomery identity [14] 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 [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.