Fekete-Szegö inequality for a subclass of analytic functions associated with Gegenbauer polynomials - Kamali, M. (Carpathian Mathematical Publications, 2022)
In this paper, we define a subclass of analytic functions by denote $T_{β}H\left( z,C_{n}^{\left( λ \right) }\left( t\right) \right)$ satisfying the following subordinate condition \begin{equation*} \left( 1-β \right) \left( \frac{zf'\left( z\right) }{f\left( z\right) }\right) +β \left( 1+\frac{zf^{′ ′}\left( z\right) }{f'\left( z\right) }\right) \prec \frac{1}{\left( 1-2tz+z^{2}\right) ^{λ }}, \end{equation*} where $β ≥ 0$, $λ ≥ 0$ and $t\in \left( \frac{1}{2},1\right] $. We give coefficient estimates and Fekete-Szegö inequality for functions belonging to this subclass.