TY  - JOUR
T1  - Applications of $k$-Fibonacci numbers for the starlike analytic functions
AU  - Sokół, Janusz
AU  - Raina, Ravinder Krishna
AU  - Yilmaz Özgür, Nihal
PY  - 2015
DA  - February
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 121
EP  - 127
VL  - 44
IS  - 1
LA  - en
AB  - 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 ofthe Fekete–Szegö problem for the class$\mathcal{S}\mathcal{L}^{k}$. An application for inversefunctions is also given.
KW  - univalent functions
KW  - convex functions
KW  - starlike functions
KW  - subordination
KW  - $k$-Fibonacci numbers
CR  - .
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UR  - https://dergipark.org.tr/en/pub/hujms/issue//524371
L1  - https://dergipark.org.tr/en/download/article-file/644752
ER  -