A theorem on the first and second local modulus of continuity and applications to quadrature rules and means

摘要

This article will focus on, and extend, the part of the earlier study that concerns with the inequalities in Theorem 1, Theorem 2 [Appl. Math. Lett. 12 (1999) 7]. In this paper, we establish a new inequality involving the first and second local modulus of continuity of a continuously differentiable function and applications to special means are investigated.