New Ostrowski type inequalities for coordinated (s,m)−convex functions in the second sense

Abstract

In the present work we introduce the class of (s,m)-convex functions on the coordinates and some new Ostrowski-type inequalities are deduced for this kind of generalized convex functions. The results obtained have the absolute value of the second partial derivative with respect to the coordinates (∂ 2 f /∂r∂t) in the aforementioned class and bounded, as a necessary condition. This generalizes the results for convex functions of [10]. Also, some corollary is presented.