Fekete-Szego problem for q-starlike functions connected with k-Fibonacci numbers
نویسندگان
چکیده
Let $\mathcal{A}$ denote the class of functions $f$ which are analytic in open unit disk $\mathbb{U}$ and given by\[f(z)=z+\sum_{n=2}^{\infty }a_{n}z^{n}\qquad \left( z\in \mathbb{U}\right) .\]The coefficient functional $\phi _{\lambda }\left( f\right) =a_{3}-\lambda a_{2}^{2}$ on $f\in \mathcal{A}$ represents various geometric quantities. For example, _{1}\left( =a_{3}-a_{2}^{2}=S_{f}\left( 0\right) /6,$ where $S_{f}$ is Schwarzian derivative. The problem maximizing absolute value $ called Fekete-Szegö problem.In a very recent paper, Shafiq \textit{et al}. [Symmetry 12:1043, 2020] defined new subclass $\mathcal{SL}\left(k,q\right), (k>0, 0<q<1) consist $f\in\mathcal{A}$ satisfying following subordination:\[\frac{z\,D_{q}f\left( z\right) }{f(z)}\prec \frac{2\tilde{p}_{k}\left(z\right) }{\left( 1+q\right) +\left( 1-q\right) \tilde{p}_{k}\left( z\right)}\qquad ,\]where\[\tilde{p}_{k}\left( =\frac{1+\tau _{k}^{2}z^{2}}{1-k\tau _{k}z-\tau_{k}^{2}z^{2}}, \qquad \tau _{k}=\frac{k-\sqrt{k^{2}+4}}{2},\]and investigated for belong to $\mathcal{SL}(k,q)$. This connected with $k$-Fibonacci numbers. main purpose this paper obtain sharp bounds f\right)$ $\mathcal{SL}\left(k,q\right)$ when both $\lambda \in \mathbb{R}$ \mathbb{C}$, improve result above mentioned paper.
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ژورنال
عنوان ژورنال: Hacettepe journal of mathematics and statistics
سال: 2022
ISSN: ['1303-5010']
DOI: https://doi.org/10.15672/hujms.1010314