Slice Spirallike Functions over Quaternions

摘要

In this paper, we study the analogue of spirallikeness for slice regular functions of one quaternionic variable. In particular, we introduce the concept of slice & gamma;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}-spirallike functions of order & alpha;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} and investigate its geometric function theory, such as coefficient estimates, growth and covering theorems. As a byproduct, the Robertson's result concerning the radii of starlikeness for holomorphic spirallike functions is generalized into slice regular functions by a very concise method, but new even for the classical case.

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