A study on Fekete-Szegö inequality for a class of analytic functions satisfying subordinate conditions associated with Chebyshev polynomials

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Article Type:
Research/Original Article (بدون رتبه معتبر)
Abstract:
We define a class of analytic functions, $A(H, n, m, \lambda)$, satisfying the following condition\begin{equation*}\frac{D_{\lambda}^{n+m} f(z)}{D_{\lambda}^{n} f(z)} \prec H(z, t),\end{equation*}where $\lambda \geq 0,n,m\in \mathbb{N}^{\ast }=\mathbb{N}\cup \{0\},t\in\left( \frac{1}{2},1\right] $ and for all $z\in \Omega $. In this study, firstly give estimates for coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $ of functions belong to this class. Furthermore, the Fekete- Szeg\"{o} inequality was examined for the functions belonging to this class.
Language:
English
Published:
Journal of Mathematical Analysis and its Contemporary Applications, Volume:7 Issue: 1, Winter 2025
Pages:
61 to 70
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