Some generalized Ostrowski–Grüss type integral inequalities

Abstract

In this paper, we establish some new Ostrowski–Grüss type integral inequalities involving $(k-1)$ interior points in 1D case, which are generalizations of some known results in the literature, and one of which is sharp. Then we deduce an Ostrowski–Grüss type integral inequality in 2D case involving ${(k-1)}^2$ interior points for the first time. We also present one application on the estimate of error bound for numerical integration formula, in which a sharp error bound for a new numerical integration formula is provided by the results established.