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


Ozdemir M. E.

APPLIED MATHEMATICS AND COMPUTATION, vol.141, no.2-3, pp.579-588, 2003 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 141 Issue: 2-3
  • Publication Date: 2003
  • Doi Number: 10.1016/s0096-3003(02)00277-1
  • Title of Journal : APPLIED MATHEMATICS AND COMPUTATION
  • Page Numbers: pp.579-588
  • Keywords: local modulus of continuity, Taylor theorem, univariate continuously differentiable functions, quadrature formulae

Abstract

This article will focus on, and extend, the part of the earlier study that concerns with the inequalities in Theorems 1 and 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. (C) 2002 Published by Elsevier Science Inc.