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Degree of approximation for bivariate Szász-Kantorovich type based on Brenke type polynomials. (English) Zbl 1476.41003

In this paper the authors introduce a Bivariate Szasz-Kantorovich type operator based on Brenke type polynomials. More exactly, the authors generalize the operators given in [F. Taşdelen et al., Abstr. Appl. Anal. 2012, Article ID 867203, 13 p. (2012; Zbl 1312.41031)] by replacing the index value \(n\) with two strictly increasing sequences \((\alpha_{n})\) and \((\beta_{n})\), where the second sequence is used at the endpoints of the integrated domain while the first sequences is used in all the other places. For this sequence initial moments and central moments are calculated and, in the main results several approximations results are proved obtaining quantitative estimates in terms of partial moduli of continuity then in terms of the complete moduli of continuity and then estimations for Lipschitz functions. Also an estimation is obtained with respect to the Peetre’s K-functional. In the final section of the paper so called Generalized Boolean Sum operators are constructed on Brenke type polynomials and several of their properties are proved.

MSC:

41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
41A63 Multidimensional problems

Citations:

Zbl 1312.41031
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Full Text: DOI

References:

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