On starlike functions connected with k-fibonacci numbers

Abstract

We present a new subclass SLk of starlike functions which is related to a shell-like curve. The coefficients of such functions are connected with k-Fibonacci numbers F-k,F- n defined recurrently by F-k,F- 0 = 0, F-k,F- 1 = 1 and F-k,F- n = kF(k, n) + F-k,F- n-1 for n = 1, where k is a given positive real number. We investigate some basic properties for the class SLk.