Applications of k-Fibonacci numbers for the starlike analytic functions

Abstract

The k-Fibonacci numbers Fk,n (k > 0), defined recursively by Fk,0 = 0,Fk,1 = 1 and Fk,n = kFk,n + Fk,n−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 Szegö problem for the class SLk. An application for inverse functions is also given. 2000 AMS Classification: Primary 30C45, secondary 30C80