Applications of $k$-Fibonacci numbers for the starlike analytic functions

Authors : Janusz SOKÓŁ, Ravinder Krishna RAİNA, Nihal YİLMAZ ÖZGÜR

Pages : 121-127

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Publication Date : 2015-02-01

Article Type : Research Paper

Abstract :The $k-$ Fibonacci numbers $F_{k,n}\:insert ignore into journalissuearticles values(k>0);$, defined recursively by $F_{k,0}=0$ , $F_{k,1}=1$ and $F_{k,n}=kF_{k,n}+F_{k,n-1}$ for $n\geq1$ are used to define a new class $\mathcal{S}\mathcal{L}^k$.  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  $\mathcal{S}\mathcal{L}^{k}$. An application for inverse functions is also given.
Keywords : univalent functions, convex functions, starlike functions, subordination, k Fibonacci numbers