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

Qing-Bo Cai, Khursheed J. Ansari, Merve Temizer Ersoy and Faruk Özger
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Qing-Bo Cai: Fujian Provincial Key Laboratory of Data-Intensive Computing, Key Laboratory of Intelligent Computing and Information Processing, School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China
Khursheed J. Ansari: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Merve Temizer Ersoy: Department of Software Engineering, Faculty of Engineering and Architecture, Nisantasi University, Istanbul 34398, Turkey
Faruk Özger: Department of Engineering Sciences, İzmir Katip Çelebi University, İzmir 35620, Turkey

Mathematics, 2022, vol. 10, issue 7, 1-20

Abstract: 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.

Keywords: Voronovskaja-type theorem; blending-type operators; ? -Bernstein operators; ? -Bernstein operators; shape parameters; statistical convergence; convergence rates; bivariate approximation; computer graphics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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