Rate of Weighted Statistical Convergence for Generalized Blending-Type Bernstein-Kantorovich Operators

Faruk Özger, Ekrem Aljimi and Merve Temizer Ersoy
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Faruk Özger: Department of Engineering Sciences, İzmir Katip Çelebi University, İzmir 35620, Turkey
Ekrem Aljimi: Faculty of Applied Sciences, Public University “Kadri Zeka”, 60000 Gjilan, Kosovo
Merve Temizer Ersoy: Faculty of Engineering and Architecture, Department of Software Engineering, Nisantasi University, Istanbul 34398, Turkey

Mathematics, 2022, vol. 10, issue 12, 1-21

Abstract: An alternative approach, known today as the Bernstein polynomials, to the Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, integral equations and computer-aided geometric design. Motivated by the improvements of Bernstein polynomials in computational disciplines, we propose a new generalization of Bernstein–Kantorovich operators involving shape parameters λ , α and a positive integer as an original extension of Bernstein–Kantorovich operators. The statistical approximation properties and the statistical rate of convergence are also obtained by means of a regular summability matrix. Using the Lipschitz-type maximal function, the modulus of continuity and modulus of smoothness, certain local approximation results are presented. Some approximation results in a weighted space are also studied. Finally, illustrative graphics that demonstrate the approximation behavior and consistency of the proposed operators are provided by a computer program.

Keywords: weighted ?-statistical convergence; shape parameter ?; shape parameter ?; blending-type operators; 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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