Bivariate q-Bernstein-Chlodowsky-Durrmeyer type operators and the associated GBS operators


Garg T., İSPİR N., Agrawal P. N.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, vol.13, no.5, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 5
  • Publication Date: 2020
  • Doi Number: 10.1142/s1793557120500916
  • Journal Name: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Keywords: Partial modulus of continuity, generalized boolean sum, Bogel continuous, Bogel differentiable, mixed modulus of smoothness, APPROXIMATION PROPERTIES, VARIANT
  • Gazi University Affiliated: Yes

Abstract

This paper deals with the approximation properties of the q-bivariate Bernstein- Chlodowsky operators of Durrmeyer type. We investigate the approximation degree of the q-bivariate operators for continuous functions in Lipschitz space and also with the help of partial modulus of continuity. Further, the Generalized Boolean Sum (GBS) operator of these bivariate q-Bernstein-Chlodowsky-Durrmeyer operators is introduced and the rate of convergence in the Bogel space of continuous functions by means of the Lipschitz class and the mixed modulus of smoothness is examined. Furthermore, the convergence and its comparisons are shown by illustrative graphics for the q-bivariate operators and the associated GBS operators to certain functions using Maple algorithms.