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Open AccessArticle

Bivariate α,q-Bernstein–Kantorovich Operators and GBS Operators of Bivariate α,q-Bernstein–Kantorovich Type

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School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China
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School of Mathematics and Computation Sciences, Anqing Normal University, Anhui 246133, China
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Department of Mathematics, Faculty of Science, Gazi University, Beşevler, Ankara 06500, Turkey
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1161; https://doi.org/10.3390/math7121161
Received: 27 August 2019 / Revised: 4 November 2019 / Accepted: 14 November 2019 / Published: 2 December 2019
(This article belongs to the Section Mathematics and Computer Science)
In this paper, we introduce a family of bivariate α , q -Bernstein–Kantorovich operators and a family of G B S (Generalized Boolean Sum) operators of bivariate α , 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 G B S operators for B-continuous and B-differentiable functions by using the mixed modulus of smoothness. View Full-Text
Keywords: α,q-Bernstein–Kantorovich operators; GBS operators; B-continuous functions; moduli of continuity; B-differentiable functions; mixed modulus of smoothness; q-integers α,q-Bernstein–Kantorovich operators; GBS operators; B-continuous functions; moduli of continuity; B-differentiable functions; mixed modulus of smoothness; q-integers
MDPI and ACS Style

Cai, Q.-B.; Cheng, W.-T.; Çekim, B. Bivariate α,q-Bernstein–Kantorovich Operators and GBS Operators of Bivariate α,q-Bernstein–Kantorovich Type. Mathematics 2019, 7, 1161.

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