@article{article_524371, title={Applications of $k$-Fibonacci numbers for the starlike analytic functions}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={44}, pages={121–127}, year={2015}, author={Sokół, Janusz and Raina, Ravinder Krishna and Yilmaz Özgür, Nihal}, keywords={univalent functions,convex functions,starlike functions,subordination,$k$-Fibonacci numbers}, abstract={The $k-$ Fibonacci numbers $F_{k,n}\:(k>0)$, defined recursively by $F_{k,0}=0$ , $F_{k,1}=1$ and $F_{k,n}=kF_{k,n}+F_{k,n-1}$ <span style="font-size:12.6px;">for $n\geq1$ are used to define a new class $\mathcal{S}\mathcal{L}^k$.  </span>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  <span style="font-size:12.6px;">$\mathcal{S}\mathcal{L}^{k}$. </span> An application for inverse
functions is also given.}, number={1}, publisher={Hacettepe University}