Parametric Generalization of the Modified Bernstein Operators


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Sofyalıoğlu M., Kanat K., ÇEKİM B.

Filomat, vol.36, no.5, pp.1699-1709, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 5
  • Publication Date: 2022
  • Doi Number: 10.2298/fil2205699s
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.1699-1709
  • Keywords: Bernstein operators, Modulus of continuity, Parametric generalization
  • Ankara Haci Bayram Veli University Affiliated: Yes

Abstract

© 2022, University of Nis. All rights reserved.The current paper deals with the parametric modification of Bernstein operators which pre-serve constant and Korovkin’s other test functions in limit case. The uniform convergence of the newly constructed operators is studied. Also, the rate of convergence is investigated by means of the modulus of continuity, by using functions which belong to Lipschitz class and by the help of Peetre’s-K functionals. Finally, some numerical examples are given to illustrate the effectiveness of the newly defined operators for computing the approximation of function.