On the F-Bernstein Polynomials

We construct a new Bernstein operator, which is called the F -Bernstein operator. This operator is obtained by using the F -factorial (Fibonacci factorial) and the Fibonomial (Fibonacci binomial). We also study the F -Bernstein basis polynomials and consider some of their properties. Moreover, we es...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2024-10, Vol.76 (6), p.937-948
Main Authors: Erdem, Alper, Dişkaya, Orhan, Menken, Hamza
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Fibonacci numbers
Geometry
Mathematics
Mathematics and Statistics
Polynomials
Statistics
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Summary:We construct a new Bernstein operator, which is called the F -Bernstein operator. This operator is obtained by using the F -factorial (Fibonacci factorial) and the Fibonomial (Fibonacci binomial). We also study the F -Bernstein basis polynomials and consider some of their properties. Moreover, we establish a relationship between the F -Bernstein polynomials and Fibonacci numbers.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-024-02364-1