Some variations of the Bohman-Korovkin theorem

Atlihan Ö. G., Gül Ince H., ORHAN C.

Mathematical and Computer Modelling, vol.50, no.7-8, pp.1205-1210, 2009 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 7-8
  • Publication Date: 2009
  • Doi Number: 10.1016/j.mcm.2009.06.009
  • Journal Name: Mathematical and Computer Modelling
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1205-1210
  • Keywords: A-statistical convergence, Fèjer's approximation theorem, Korovkin type theorem, Matrix summability method, Sequence of positive linear operators, Weierstrass' approximation theorem
  • Ankara University Affiliated: Yes

Abstract

In this paper we develop the main aspects of the Bohman-Korovkin theorem on approximation of continuous functions with the use of A-statistical convergence and matrix summability method which includes both convergence and almost convergence. Since statistical convergence and almost convergence methods are incompatible we conclude that these methods can be used alternatively to get some approximation results. © 2009 Elsevier Ltd. All rights reserved.