Approximation of B-continuous and B-differentiable functions by GBS operators of q-Bernstein-Schurer-Stancu type

Sidharth M., İSPİR N., Agrawal P. N.

TURKISH JOURNAL OF MATHEMATICS, vol.40, no.6, pp.1298-1315, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 6
  • Publication Date: 2016
  • Doi Number: 10.3906/mat-1509-66
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1298-1315
  • Keywords: q-Bernstein-Schurer-Stancu operators, partial moduli of continuity, B-continuous, B-differentiable, GBS operators, modulus of smoothness, degree of approximation, K-FUNCTIONALS, SMOOTHNESS
  • Gazi University Affiliated: Yes

Abstract

Barbosu and Muraru (2015) introduced the bivariate generalization of the q-Bernstein-Schurer-Stancu operators and constructed a GBS operator of q-Bernstein-Schurer-Stancu type. The concern of this paper is to obtain the rate of convergence in terms of the partial and complete modulus of continuity and the degree of approximation by means of Lipschitz-type class for the bivariate operators. In the last section we estimate the degree of approximation by means of Lipschitz class function and the rate of convergence with the help of mixed modulus of smoothness for the GBS operator of q-Bernstein-Schurer-Stancu type. Furthermore, we show comparisons by some illustrative graphics in Maple for the convergence of the operators to some functions.