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Statistical Blending-Type Approximation by a Class of Operators That Includes Shape Parameters λ and α

This paper is devoted to studying the statistical approximation properties of a sequence of univariate and bivariate blending-type Bernstein operators that includes shape parameters α and λ and a positive integer. An estimate of the corresponding rates was obtained, and a Voronovskaja-type theorem i...

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Bibliographic Details
Published in:Mathematics (Basel) 2022-04, Vol.10 (7), p.1149
Main Authors: Cai, Qing-Bo, Ansari, Khursheed J., Temizer Ersoy, Merve, Özger, Faruk
Format: Article
Language:English
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Summary:This paper is devoted to studying the statistical approximation properties of a sequence of univariate and bivariate blending-type Bernstein operators that includes shape parameters α and λ and a positive integer. An estimate of the corresponding rates was obtained, and a Voronovskaja-type theorem is given by a weighted A-statistical convergence. A Korovkin-type theorem is provided for the univariate and bivariate cases of the blending-type operators. Moreover, the convergence behavior of the univariate and bivariate new blending basis and new blending operators are exhaustively demonstrated by computer graphics. The studied univariate and bivariate blending-type operators reduce to the well-known Bernstein operators in the literature for the special cases of shape parameters α and λ, and they propose better approximation results.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10071149