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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 141 Issue: 2-3
  • Publication Date: 2003
  • Doi Number: 10.1016/s0096-3003(02)00277-1
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.579-588
  • Keywords: local modulus of continuity, Taylor theorem, univariate continuously differentiable functions, quadrature formulae
  • Bursa Uludag University Affiliated: Yes

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.