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

Kamali, Muhammet

doi:10.30495/maca.2025.2049601.1119

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

10.30495/maca.2025.2049601.1119

Volume 7, Issue 1
Winter 2025

Pages 61-70

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Author

Muhammet Kamali

Department of Mathematics, Faculty of Sciences, Kyrgyz-Turkish Mans University, Chyngz Aitmatov Avenue, Biskek, Kyrgyz Republic

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.

Keywords

Analytic function

Salagean Operator

Coefficient estimates

Fekete-Szegö inequality

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