On Starlike Functions Connected with $$k$$k-Fibonacci Numbers

We present a new subclass $$\mathcal {SL}^{k}$$SLk of starlike functions which is related to a shell-like curve. The coefficients of such functions are connected with $$k$$k-Fibonacci numbers $$F_{k,n}$$Fk,n defined recurrently by $$ F_{k,0}=0,F_{k,1}=1$$Fk,0=0,Fk,1=1 and $$F_{k,n}=kF_{k,n}+F_{k,n-1}$$Fk,n=kFk,n+Fk,n-1 for $$n\ge 1$$n≥1, where $$ k $$k is a given positive real number. We investigate some basic properties for the class $$\mathcal {SL}^{k}$$SLk.