Some New Results on Bicomplex Bernstein Polynomials

The aim of this work is to consider bicomplex Bernstein polynomials attached to analytic functions on a compact <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck"&...

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Autores principales:	Carlo Cattani, Çíğdem Atakut, Özge Özalp Güller, Seda Karateke
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	bicomplex Bernstein polynomials analytic functions holomorphic functions Voronovskaja-type theorem Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/16542b7d8f224a1d83eafea99b97a743
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spelling	oai:doaj.org-article:16542b7d8f224a1d83eafea99b97a7432021-11-11T18:17:46ZSome New Results on Bicomplex Bernstein Polynomials10.3390/math92127482227-7390https://doaj.org/article/16542b7d8f224a1d83eafea99b97a7432021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2748https://doaj.org/toc/2227-7390The aim of this work is to consider bicomplex Bernstein polynomials attached to analytic functions on a compact <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">C</mi><mn>2</mn></msub></semantics></math></inline-formula>-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.Carlo CattaniÇíğdem AtakutÖzge Özalp GüllerSeda KaratekeMDPI AGarticlebicomplex Bernstein polynomialsanalytic functionsholomorphic functionsVoronovskaja-type theoremMathematicsQA1-939ENMathematics, Vol 9, Iss 2748, p 2748 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	bicomplex Bernstein polynomials analytic functions holomorphic functions Voronovskaja-type theorem Mathematics QA1-939
spellingShingle	bicomplex Bernstein polynomials analytic functions holomorphic functions Voronovskaja-type theorem Mathematics QA1-939 Carlo Cattani Çíğdem Atakut Özge Özalp Güller Seda Karateke Some New Results on Bicomplex Bernstein Polynomials
description	The aim of this work is to consider bicomplex Bernstein polynomials attached to analytic functions on a compact <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">C</mi><mn>2</mn></msub></semantics></math></inline-formula>-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.
format	article
author	Carlo Cattani Çíğdem Atakut Özge Özalp Güller Seda Karateke
author_facet	Carlo Cattani Çíğdem Atakut Özge Özalp Güller Seda Karateke
author_sort	Carlo Cattani
title	Some New Results on Bicomplex Bernstein Polynomials
title_short	Some New Results on Bicomplex Bernstein Polynomials
title_full	Some New Results on Bicomplex Bernstein Polynomials
title_fullStr	Some New Results on Bicomplex Bernstein Polynomials
title_full_unstemmed	Some New Results on Bicomplex Bernstein Polynomials
title_sort	some new results on bicomplex bernstein polynomials
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/16542b7d8f224a1d83eafea99b97a743
work_keys_str_mv	AT carlocattani somenewresultsonbicomplexbernsteinpolynomials AT cigdematakut somenewresultsonbicomplexbernsteinpolynomials AT ozgeozalpguller somenewresultsonbicomplexbernsteinpolynomials AT sedakarateke somenewresultsonbicomplexbernsteinpolynomials
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Some New Results on Bicomplex Bernstein Polynomials

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