New subclasses of analytic and bi-univalent functions endowed with coefficient estimate problems

By Feras Yousef, Somaia Alroud, Mohamed Illafe. Analysis and Mathematical Physics, 2018

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Inspired by the recent works of Srivastava et al. (Appl Math Lett 23(10):1188–1192, 2010), Frasin and Aouf (Appl Math Lett 24(9):1569–1573, 2011), and Çağlar et al. (Filomat 27(7):1165–1171, 2013), we introduce and investigate in the present paper two new general subclasses of the class consisting of normalized analytic and bi-univalent functions in the open unit disk U={z∈C:z<1}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {U}}=\{z\in {\mathbb {C}}:\left| z\right| <1\}$$\end{document}. For functions belonging to these general subclasses introduced here, we obtain estimates on the Taylor–Maclaurin coefficients |a2|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|a_{2}|$$\end{document} and |a3|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|a_{3}|$$\end{document}. Several connections to some of the earlier known results are also pointed out. The results presented in this paper would generalize and improve those in related works of several earlier authors.

Subfields: Applied Mathematics, Geometry and Topology, Immunology

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