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Baxhaku, Behar; Agrawal, Purshottam Narain

Degree of approximation for bivariate extension of Chlodowsky-type \(q\)-Bernstein-Stancu-Kantorovich operators. (English) Zbl 1411.41007

Appl. Math. Comput. 306, 56-72 (2017).
Summary: We introduce the bivariate generalization of the Chlodowsky-type \(q\)-Bernstein-Stancu-Kantorovich operators on an unbounded domain and studied the rate of convergence in terms of the Lipschitz class function and complete modulus of continuity. Further, we establish the weighted approximation properties for these operators. The aim of this paper is to obtain the degree of approximation for these bivariate operators in terms of the partial moduli of continuity and the Peetre’s K-functional. Then, we give generalization of the operators and investigate their approximations. Furthermore, we show the convergence of the bivariate Chlodowsky-type operators to certain functions by illustrative graphics using Python programming language. Finally, we construct the GBS operators of bivariate Chlodowsky-type \(q\)-Bernstein-Stancu-Kantorovich and estimate the rate of convergence for these operators with the help of mixed modulus of smoothness.

Cited in 14 Documents

MSC:

41A10 Approximation by polynomials
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
26A16 Lipschitz (Hölder) classes
41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
41A63 Multidimensional problems

Keywords:

\(q\)-Bernstein-Stancu-Kantorovich operators; partial moduli of continuity; weighted approximation; B-continuous; B-differentiable; GBS operators

Software:

Python
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Full Text: DOI

References:

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