On the $F$-Bernstein polynomials - Erdem, Alper; Dişkaya, Orhan; Menken, Hamza (Ukrains’kyi Matematychnyi Zhurnal, 2024)
UDC 517.5We 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.