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Fekete-szegö results for certain class of meromorphic functions using q-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q-$$\end{document}derivative operatorFekete-Szegö Results for certain class of meromorphic functions...A. O. Mostafa, G. M. El-Hawsh
被引：0
作者：
A. O. Mostafa
[1
]
G. M. El-Hawsh
[2
]
机构：
[1] Mansoura University,Department of Mathematics, Faculty of Science
[2] Fayoum University,Department of Mathematics, Faculty of Science
关键词：
Analytic function;
Subordination;
Fekete-Szegö problem;
Meromorphic function;
derivative operator;
30C45;
D O I：
10.1007/s13370-024-01223-3
中图分类号：
学科分类号：
摘要：
In the present paper, we introduce the subclasses ∑b∗q,ϕ\documentclass[12pt]{minimal}
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\begin{document}$$\sum _{b}^{*}\left( q,\phi \right) $$\end{document} and ∑b∗α,q,ϕ\documentclass[12pt]{minimal}
\usepackage{amsmath}
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\begin{document}$$\sum _{b}^{*}\left( \alpha ,q,\phi \right) $$\end{document} of meromorphic functions fz\documentclass[12pt]{minimal}
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\begin{document}$$f\left( z\right) $$\end{document} satisfying 1+1b-qzDq∗f(z)f(z)-1≺ϕ(z)\documentclass[12pt]{minimal}
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\begin{document}$$1+\frac{1}{b}\left[ -\frac{qzD_{q}^{*}f(z)}{f(z)}-1\right] \prec \phi (z)$$\end{document} and 1+1b-1-αqqzDq∗fz+αqzDq∗zDq∗fz1-αqfz-αzDq∗fz-1≺ϕ(z)(b∈C∗=C\0,\documentclass[12pt]{minimal}
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\begin{document}$$1+\frac{1}{b}\left[ \frac{-\left( 1-\frac{\alpha }{q}\right) qzD_{q}^{*}f\left( z\right) +\alpha qzD_{q}^{*}\left[ zD_{q}^{*}f\left( z\right) \right] }{\left( 1-\frac{\alpha }{q}\right) f\left( z\right) -\alpha zD_{q}^{*}f\left( z\right) }-1\right] \prec \phi (z)\ (b\in \mathbb {C} ^{*}=\mathbb {C}\backslash \left\{ 0\right\} ,\ $$\end{document}α∈C\(0,1],Re(α)≥0,0<q<1)\documentclass[12pt]{minimal}
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\begin{document}$$\alpha \in \mathbb {C}\backslash (0,1],\ \operatorname {Re}(\alpha )\ge 0,\ 0<q<1)$$\end{document}, respectively. Sharp bounds for the Fekete-Szegö functional a1-μa02\documentclass[12pt]{minimal}
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\begin{document}$$\left| a_{1}-\mu a_{0}^{2}\right| $$\end{document} are obtained.
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