The Schwarz-Pick theorem and its applications

M. A. Qazi, Q. I. Rahman

Abstract


Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz-Pick theorem from the geometric theory of functions. We also use the Phragmen-Lindelof principle, which is of course standard in such situations.

Keywords


Bernstein’s inequality; functions of exponential type in a half-plane; rational functions; Schwarz-Pick theorem

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References


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DOI: http://dx.doi.org/10.2478/v10062-011-0021-6
Date of publication: 2016-07-27 21:54:12
Date of submission: 2016-07-27 13:55:31


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