Geodesic
The Schwarz-Pick theorem and its applications
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 2.

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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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Qazi, M. A.; Rahman, Q. I. The Schwarz-Pick theorem and its applications. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 2. http://geodesic.mathdoc.fr/item/AUM_2011_65_2_a16/

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