Fekete-Szegö problem for $q$-starlike functions in connected with $k$-Fibonacci numbers

Authors : Serap BULUT

Pages : 1661-1673

Doi:10.15672/hujms.1010314

View : 28 | Download : 9

Publication Date : 2022-12-01

Article Type : Research Paper

Abstract :Let $\mathcal{A}$ denote the class of functions $f$ which are analytic in the open unit disk $\mathbb{U}$ and given by \[ finsert ignore into journalissuearticles values(z);=z+\sum_{n=2}^{\infty }a_{n}z^{n}\qquad \leftinsert ignore into journalissuearticles values( z\in \mathbb{U}\right); . \] The coefficient functional $\phi _{\lambda }\leftinsert ignore into journalissuearticles values( f\right); =a_{3}-\lambda a_{2}^{2}$ on $f\in \mathcal{A}$ represents various geometric quantities. For example, $\phi _{1}\leftinsert ignore into journalissuearticles values( f\right); =a_{3}-a_{2}^{2}=S_{f}\leftinsert ignore into journalissuearticles values( 0\right); /6,$ where $S_{f}$ is the Schwarzian derivative. The problem of maximizing the absolute value of the functional $\phi _{\lambda }\leftinsert ignore into journalissuearticles values( f\right); $ is called the Fekete-Szegö problem. In a very recent paper, Shafiq \textit{et al}. [Symmetry 12:1043, 2020] defined a new subclass $\mathcal{SL}\leftinsert ignore into journalissuearticles values(k,q\right);, insert ignore into journalissuearticles values(k>0, 0 Keywords : analytic function, univalent function, shell like function, Fekete Szegö problem, Fibonacci numbers, subordination

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