On the F -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.