On the $F$-Bernstein polynomials
UDC 517.5 We construct a new Bernstein operator, which is called the $F$-Bernstein operator obtained by using the $F$-factorial (Fibonacci factorial) and the Fibonomial (Fibonacci binomial). Then we examine the $F$-Bernstein basis polynomials and some of their properties. M...
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| Datum: | 2024 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2024
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7439 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512671424577536 |
|---|---|
| author | Erdem, Alper Dişkaya, Orhan Menken, Hamza Erdem, Alper Dişkaya, Orhan Menken, Hamza |
| author_facet | Erdem, Alper Dişkaya, Orhan Menken, Hamza Erdem, Alper Dişkaya, Orhan Menken, Hamza |
| author_sort | Erdem, Alper |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-07-15T03:05:01Z |
| description | UDC 517.5
We construct a new Bernstein operator, which is called the $F$-Bernstein operator obtained by using the $F$-factorial (Fibonacci factorial) and the Fibonomial (Fibonacci binomial). Then we examine the $F$-Bernstein basis polynomials and some of their properties. Moreover, we acquire certain connection between the $F$-Bernstein polynomials and the Fibonacci numbers.   |
| doi_str_mv | 10.3842/umzh.v76i5.7439 |
| first_indexed | 2026-03-24T03:32:30Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7439 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:30Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-74392024-07-15T03:05:01Z On the $F$-Bernstein polynomials On the $F$-Bernstein polynomials Erdem, Alper Dişkaya, Orhan Menken, Hamza Erdem, Alper Dişkaya, Orhan Menken, Hamza Fibonacci numbers Bernstein polynomials 11B39 47A50 26C05 UDC 517.5 We construct a new Bernstein operator, which is called the $F$-Bernstein operator obtained by using the $F$-factorial (Fibonacci factorial) and the Fibonomial (Fibonacci binomial). Then we examine the $F$-Bernstein basis polynomials and some of their properties. Moreover, we acquire certain connection between the $F$-Bernstein polynomials and the Fibonacci numbers.   УДК 517.5 Про $F$-поліноми Бернштейна Побудовано новий оператор Бернштейна, що називається $F$-оператором Бернштейна. Цей оператор отримано за допомогою $F$-факторіала (факторіала Фібоначчі) та фібонома (бінома Фібоначчі).  Крім того,   розглянуто базисні $F$-поліноми Бернштейна та деякі  їхні властивості. Навіть більше, отримано певний зв'язок між $F$-поліномами Бернштейна та числами Фібоначчі. Institute of Mathematics, NAS of Ukraine 2024-07-03 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7439 10.3842/umzh.v76i5.7439 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 6 (2024); 832–842 Український математичний журнал; Том 76 № 6 (2024); 832–842 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7439/10030 Copyright (c) 2024 Orhan Dişkaya, Hamza Menken, Alper Erdem |
| spellingShingle | Erdem, Alper Dişkaya, Orhan Menken, Hamza Erdem, Alper Dişkaya, Orhan Menken, Hamza On the $F$-Bernstein polynomials |
| title | On the $F$-Bernstein polynomials |
| title_alt | On the $F$-Bernstein polynomials |
| title_full | On the $F$-Bernstein polynomials |
| title_fullStr | On the $F$-Bernstein polynomials |
| title_full_unstemmed | On the $F$-Bernstein polynomials |
| title_short | On the $F$-Bernstein polynomials |
| title_sort | on the $f$-bernstein polynomials |
| topic_facet | Fibonacci numbers Bernstein polynomials 11B39 47A50 26C05 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7439 |
| work_keys_str_mv | AT erdemalper onthefbernsteinpolynomials AT diskayaorhan onthefbernsteinpolynomials AT menkenhamza onthefbernsteinpolynomials AT erdemalper onthefbernsteinpolynomials AT diskayaorhan onthefbernsteinpolynomials AT menkenhamza onthefbernsteinpolynomials |