Korovkin type approximation of Abel transforms of q-Meyer-Konig and Zeller operators

Soylemez D., ÜNVER M.

INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, vol.11, no.2, pp.339-350, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.22075/ijnaa.2019.17520.1944
  • Journal Name: INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.339-350
  • Keywords: Meyer-Konig and Zeller Operators, Abel convergence, Rate of convergence, STATISTICAL APPROXIMATION, LINEAR-OPERATORS, WEIGHTED SPACES, THEOREMS, SUMMABILITY, CONVERGENCE
  • Ankara University Affiliated: Yes

Abstract

In this paper we investigate some Korovkin type approximation properties of the q-Meyer-Konig and Zeller operators and Durrmeyer variant of the q-Meyer-Konig and Zeller operators via Abel summability method which is a sequence-to-function transformation and which extends the ordinary convergence. We show that the approximation results obtained in this paper are more general than some previous results. We also obtain the rate of Abel convergence for the corresponding operators. Finally, we conclude our results with some graphical analysis.