On the $F$-Bernstein polynomials

Alper Erdem; Orhan Dişkaya; Hamza Menken

doi:10.3842/umzh.v76i5.7439

Alper Erdem Department of Mathematics, Mersin University, Turkey
Orhan Dişkaya Department of Mathematics, Mersin University, Turkey
Hamza Menken Department of Mathematics, Mersin University, Turkey

DOI: https://doi.org/10.3842/umzh.v76i5.7439

Keywords: Fibonacci numbers, Bernstein polynomials

Abstract

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.

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