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

Cai Q., Cheng W., ÇEKİM B.

MATHEMATICS, cilt.7, sa.12, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7 Sayı: 12
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3390/math7121161
  • Dergi Adı: MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: 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 Üniversitesi Adresli: Evet

Özet

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.