Some New Results on Bicomplex Bernstein Polynomials

Carlo Cattani, Çíğdem Atakut, Özge Özalp Güller and Seda Karateke
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Carlo Cattani: Engineering School, DEIM, Tuscia University, 01100 Viterbo, Italy
Çíğdem Atakut: Department of Mathematics, Ankara University, Ankara 06100, Turkey
Özge Özalp Güller: Department of Mathematics, Ankara University, Ankara 06100, Turkey
Seda Karateke: Department of Computer Engineering, Istanbul Ayvansaray University, Istanbul 34087, Turkey

Mathematics, 2021, vol. 9, issue 21, 1-18

Abstract: The aim of this work is to consider bicomplex Bernstein polynomials attached to analytic functions on a compact C 2 -disk and to present some approximation properties extending known approximation results for the complex Bernstein polynomials. Furthermore, we obtain and present quantitative estimate inequalities and the Voronovskaja-type result for analytic functions by bicomplex Bernstein polynomials.

Keywords: bicomplex Bernstein polynomials; analytic functions; holomorphic functions; Voronovskaja-type theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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