Abel transforms of positive linear operators on weighted spaces

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Unver M.

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, no.5, pp.813-822, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2014
  • Doi Number: 10.36045/bbms/1420071855
  • Journal Name: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.813-822
  • Keywords: Abel convergence, sequence of positive linear operators, the Korovkin approximation theorem, weight function, weighted space, APPROXIMATION, CONVERGENCE, SUMMABILITY
  • Ankara University Affiliated: Yes

Abstract

The classical Korovkin approximation theory deals with the convergence of a sequence of positive linear operators. When the sequence of positive linear operators does not converge it will be useful to use some summability methods. In this paper we use the Abel method, a sequence-to-function transformation, to study a Korovkin type approximation theorem for positive linear operators acting from a weighted space C-rho 1 into a weighted space B-rho 2. Moreover using the modulus of continuity we also give rate of Abel convergence.