- Hacettepe Journal of Mathematics and Statistics
- Vol: 44 Issue: 1
- Applications of $k$-Fibonacci numbers for the starlike analytic functions
Applications of $k$-Fibonacci numbers for the starlike analytic functions
Authors : Janusz Sokół, Ravinder Krishna Raina, Nihal Yilmaz Özgür
Pages : 121-127
View : 16 | Download : 5
Publication Date : 2015-02-01
Article Type : Research
Abstract :The $k-$ Fibonacci numbers $F_{k,n}\:(k>0)$, defined recursively by $F_{k,0}=0$ , $F_{k,1}=1$ and $F_{k,n}=kF_{k,n}+F_{k,n-1}$ 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