Approximation by bivariate generalized Bernstein–Schurer operators and associated GBS operators

We construct the bivariate form of Bernstein–Schurer operators based on parameter α . We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K -functional of our newly defined operators. Moreover, we define the associated generalized B...

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Veröffentlicht in:	Advances in difference equations Jg. 2020; H. 1; S. 1 - 17
1. Verfasser:	Mohiuddine, S. A.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Cham Springer International Publishing 01.12.2020 Springer Nature B.V SpringerOpen
Schlagworte:	Analysis Applications Approximation Bivariate analysis Bivariate α-Bernstein–Schurer operators Boolean algebra Bögel differentiable function Difference and Functional Equations Functional Analysis GBS operators Mathematical analysis Mathematics Mathematics and Statistics Methods Modulus of continuity Operators Ordinary Differential Equations Partial Differential Equations Smoothness Topics in Special Functions and q-Special Functions: Theory α-Bernstein operators Bernstein operators Bögel differentiable function 41A25 41A36 Bivariate GBS operators 41A10 Bernstein–Schurer operators Modulus of continuity
ISSN:	1687-1847, 1687-1839, 1687-1847
Online-Zugang:	Volltext
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Zusammenfassung:	We construct the bivariate form of Bernstein–Schurer operators based on parameter α . We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K -functional of our newly defined operators. Moreover, we define the associated generalized Boolean sum (shortly, GBS) operators and estimate the rate of convergence by means of mixed modulus of smoothness. Finally, the order of approximation for Bögel differentiable function of our GBS operators is presented.
Bibliographie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1687-1847 1687-1839 1687-1847
DOI:	10.1186/s13662-020-03125-7