A summability process on Baskakov-type approximation

Aslan I., Duman O.

PERIODICA MATHEMATICA HUNGARICA, vol.72, no.2, pp.186-199, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.1007/s10998-016-0120-9
  • Journal Name: PERIODICA MATHEMATICA HUNGARICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.186-199
  • Keywords: Summability process, Baskakov-type approximation, The Korovkin theory, POSITIVE LINEAR-OPERATORS, CONVERGENCE
  • Hacettepe University Affiliated: No

Abstract

The summability process introduced by Bell (Proc Am Math Soc 38: 548-552, 1973) is a more general and also weaker method than ordinary convergence. Recent studies have demonstrated that using this convergence in classical approximation theory provides many advantages. In this paper, we study the summability process to approximate a function and its derivatives by means of a wider class of linear operators than a family of positive linear operators. Our results improve not only Baskakov's idea in (Mat Zametki 13: 785-794, 1973) but also the Korovkin theory based on positive linear operators. In order to verify this we display a specific sequence of approximating operators by plotting their graphs.