Abstract:

Let $\mathcal{A}$ denote the class of functions $f$ which are analytic in the 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, $\phi _{1}\left( f\right) =a_{3}-a_{2}^{2}=S_{f}\left( 0\right) /6,$ where $S_{f}$ is the Schwarzian derivative. The problem of maximizing the absolute value of the functional $\phi _{\lambda }\left( 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}\left(k,q\right), (k>0, 0

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