New Generalized 2D Ostrowski type inequalities on time scales with $k^2$ points using a parameter

Abstract

Recently, a new Ostrowski type inequality on time scales for $k$ points was proved in [G. Xu, Z. B. Fang: A Generalization of Ostrowski type inequality on time scales with $k$ points. Journal of Mathematical Inequalities (2017), 11(1):41--48]. In this article, we extend this result to the 2-dimensional case. Besides extension, our results also generalize the three main results of Meng and Feng in the paper [Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables. Journal of Inequalities and Applications (2012), 1:74]. In addition, we apply some of our theorems to the continuous, discrete, and quantum calculus to obtain more interesting results in this direction. We hope that results obtained in this paper would find their place in approximation and numerical analysis.