Bivariate alpha,q-Bernstein-Kantorovich Operators and GBS Operators of Bivariate alpha,q-Bernstein-Kantorovich Type

Cai Q., Cheng W., ÇEKİM B.

MATHEMATICS, vol.7, no.12, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 12
  • Publication Date: 2019
  • Doi Number: 10.3390/math7121161
  • Journal Name: MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: alpha,q-Bernstein-Kantorovich operators, GBS operators, B-continuous functions, moduli of continuity, B-differentiable functions, mixed modulus of smoothness, q-integers, APPROXIMATION PROPERTIES, CONVERGENCE
  • Gazi University Affiliated: Yes


In this paper, we introduce a family of bivariate alpha, q-Bernstein-Kantorovich operators and a family of GBS (Generalized Boolean Sum) operators of bivariate alpha, q-Bernstein-Kantorovich type. For the former, we obtain the estimate of moments and central moments, investigate the degree of approximation for these bivariate operators in terms of the partial moduli of continuity and Peetre's K-functional. For the latter, we estimate the rate of convergence of these GBS operators for B-continuous and B-differentiable functions by using the mixed modulus of smoothness.