Fekete-Szegö inequality for a subclass of analytic functions associated with Gegenbauer polynomials

  • M. Kamali Kyrgyz-Turkish Manas University, Chyngyz Aitmatov Av., Bishkek, Kyrgyz Republic
Keywords: analytic and univalent function, typically real function, subordination, Gegenbauer polynomial, coefficient estimate, Fekete-Szegö inequality
Published online: 2022-12-30


In this paper, we define a subclass of analytic functions by denote $T_{\beta}H\left( z,C_{n}^{\left( \lambda \right) }\left( t\right) \right)$ satisfying the following subordinate condition \begin{equation*} \left( 1-\beta \right) \left( \frac{zf'\left( z\right) }{f\left( z\right) }\right) +\beta \left( 1+\frac{zf^{\prime \prime}\left( z\right) }{f'\left( z\right) }\right) \prec \frac{1}{\left( 1-2tz+z^{2}\right) ^{\lambda }}, \end{equation*} where $\beta \geq 0$, $\lambda \geq 0$ and $t\in \left( \frac{1}{2},1\right] $. We give coefficient estimates and Fekete-Szegö inequality for functions belonging to this subclass.

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How to Cite
Kamali M. Fekete-Szegö Inequality for a Subclass of Analytic Functions Associated With Gegenbauer Polynomials. Carpathian Math. Publ. 2022, 14 (2), 582-591.