A note on [Formula: see text] -Bernstein polynomials and their applications based on [Formula: see text] -calculus

Nowadays [Formula: see text] -Bernstein polynomials have been studied in many different fields such as operator theory, CAGD, and number theory. In order to obtain the fundamental properties and results of Bernstein polynomials by using [Formula: see text] -calculus, we give basic definitions and re...

Descripción completa

Detalles Bibliográficos
Autores principales: Agyuz, Erkan, Acikgoz, Mehmet
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5893731/
https://www.ncbi.nlm.nih.gov/pubmed/29670323
http://dx.doi.org/10.1186/s13660-018-1673-3
_version_ 1783313363955089408
author Agyuz, Erkan
Acikgoz, Mehmet
author_facet Agyuz, Erkan
Acikgoz, Mehmet
author_sort Agyuz, Erkan
collection PubMed
description Nowadays [Formula: see text] -Bernstein polynomials have been studied in many different fields such as operator theory, CAGD, and number theory. In order to obtain the fundamental properties and results of Bernstein polynomials by using [Formula: see text] -calculus, we give basic definitions and results related to [Formula: see text] -calculus. The main purpose of this study is to investigate a generating function for [Formula: see text] -Bernstein polynomials. By using an approach similar to that of Goldman et al. in (SIAM J. Discrete Math. 28(3):1009-1025, 2014), we derive some new identities, relations, and formulas for the [Formula: see text] -Bernstein polynomials. Also, we give a plot generating function of [Formula: see text] -Bernstein polynomials for some selected p and q values.
format Online
Article
Text
id pubmed-5893731
institution National Center for Biotechnology Information
language English
publishDate 2018
publisher Springer International Publishing
record_format MEDLINE/PubMed
spelling pubmed-58937312018-04-16 A note on [Formula: see text] -Bernstein polynomials and their applications based on [Formula: see text] -calculus Agyuz, Erkan Acikgoz, Mehmet J Inequal Appl Research Nowadays [Formula: see text] -Bernstein polynomials have been studied in many different fields such as operator theory, CAGD, and number theory. In order to obtain the fundamental properties and results of Bernstein polynomials by using [Formula: see text] -calculus, we give basic definitions and results related to [Formula: see text] -calculus. The main purpose of this study is to investigate a generating function for [Formula: see text] -Bernstein polynomials. By using an approach similar to that of Goldman et al. in (SIAM J. Discrete Math. 28(3):1009-1025, 2014), we derive some new identities, relations, and formulas for the [Formula: see text] -Bernstein polynomials. Also, we give a plot generating function of [Formula: see text] -Bernstein polynomials for some selected p and q values. Springer International Publishing 2018-04-10 2018 /pmc/articles/PMC5893731/ /pubmed/29670323 http://dx.doi.org/10.1186/s13660-018-1673-3 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Agyuz, Erkan
Acikgoz, Mehmet
A note on [Formula: see text] -Bernstein polynomials and their applications based on [Formula: see text] -calculus
title A note on [Formula: see text] -Bernstein polynomials and their applications based on [Formula: see text] -calculus
title_full A note on [Formula: see text] -Bernstein polynomials and their applications based on [Formula: see text] -calculus
title_fullStr A note on [Formula: see text] -Bernstein polynomials and their applications based on [Formula: see text] -calculus
title_full_unstemmed A note on [Formula: see text] -Bernstein polynomials and their applications based on [Formula: see text] -calculus
title_short A note on [Formula: see text] -Bernstein polynomials and their applications based on [Formula: see text] -calculus
title_sort note on [formula: see text] -bernstein polynomials and their applications based on [formula: see text] -calculus
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5893731/
https://www.ncbi.nlm.nih.gov/pubmed/29670323
http://dx.doi.org/10.1186/s13660-018-1673-3
work_keys_str_mv AT agyuzerkan anoteonformulaseetextbernsteinpolynomialsandtheirapplicationsbasedonformulaseetextcalculus
AT acikgozmehmet anoteonformulaseetextbernsteinpolynomialsandtheirapplicationsbasedonformulaseetextcalculus
AT agyuzerkan noteonformulaseetextbernsteinpolynomialsandtheirapplicationsbasedonformulaseetextcalculus
AT acikgozmehmet noteonformulaseetextbernsteinpolynomialsandtheirapplicationsbasedonformulaseetextcalculus

Ejemplares similares