Approximation by bivariate Chlodowsky type Szász–Durrmeyer operators and associated GBS operators on weighted spaces


Aslan R., Mursaleen M.

Journal of Inequalities and Applications, vol.2022, no.1, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2022 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1186/s13660-022-02763-7
  • Journal Name: Journal of Inequalities and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Degree of approximation, GBS type operators, Lipschitz type functions, Mixed modulus of continuity, Weighted approximation
  • Van Yüzüncü Yıl University Affiliated: No

Abstract

In this article, we consider a bivariate Chlodowsky type Szász–Durrmeyer operators on weighted spaces. We obtain the rate of approximation in connection with the partial and complete modulus of continuity and also for the elements of the Lipschitz type class. Moreover, we examine the degree of convergence with regard to the weighted modulus of continuity and Peetre’s K-functional. Further, we construct the associated GBS type of these operators and estimate the degree of approximation using the mixed modulus of continuity and a class of the Lipschitz of Bögel type continuous functions. Finally, with the help of Maple software, we present the comparisons of the convergence of the bivariate Chlodowsky type Szász–Durrmeyer operators and associated GBS type operators to certain functions with some graphs and error estimation tables.