Applications of k-fibonacci numbers for the starlike analytic functions

Abstract

The k-Fibonacci numbers F-k,F-n (k > 0), defined recursively by F-k; 0 = 0; F-k,F-1 = 1 and F-k,F-n = k F-k,F-n + F(k, n-1)1 for n >= 1 are used to define a new class SLk. The purpose of this paper is to apply properties of k-Fibonacci numbers to consider the classical problem of estimation of the Fekete-Szego problem for the class SLk. An application for inverse functions is also given.