The Schwarz-Pick theorem and its applications
Annales UMCS, Mathematica (2011)
- Volume: 65, Issue: 2, page 149-167
- ISSN: 2083-7402
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topM. Qazi, and Q. Rahman. "The Schwarz-Pick theorem and its applications." Annales UMCS, Mathematica 65.2 (2011): 149-167. <http://eudml.org/doc/267558>.
@article{M2011,
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 Phragmén-Lindelöf principle, which is of course standard in such situations.},
author = {M. Qazi, Q. Rahman},
journal = {Annales UMCS, Mathematica},
keywords = {Bernstein's inequality; functions of exponential type in a half-plane; rational functions; Schwarz-Pick theorem},
language = {eng},
number = {2},
pages = {149-167},
title = {The Schwarz-Pick theorem and its applications},
url = {http://eudml.org/doc/267558},
volume = {65},
year = {2011},
}
TY - JOUR
AU - M. Qazi
AU - Q. Rahman
TI - The Schwarz-Pick theorem and its applications
JO - Annales UMCS, Mathematica
PY - 2011
VL - 65
IS - 2
SP - 149
EP - 167
AB - 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 Phragmén-Lindelöf principle, which is of course standard in such situations.
LA - eng
KW - Bernstein's inequality; functions of exponential type in a half-plane; rational functions; Schwarz-Pick theorem
UR - http://eudml.org/doc/267558
ER -
References
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- Krzyż, J. G., Problems in Complex Variable Theory, American Elsevier Publishing Company, Inc., New York, 1971. Zbl0239.30001
- Qazi, M. A., Rahman, Q. I., Some estimates for the derivatives of rational functions, Comput. Methods Funct. Theory 10 (2010), 61-79. Zbl1194.30030
- Qazi, M. A., Rahman, Q. I., Functions of exponential type in a half-plane, Complex Var. Elliptic Equ. (in print). Zbl1291.30006
- Rahman, Q. I., Inequalities concerning polynomials and trigonometric polynomials, J. Math. Anal. Appl. 6 (1963), 303-324. Zbl0122.25302
- Rahman, Q. I., Schmeisser, G., Analytic Theory of Polynomials, Clarendon Press, Oxford, 2002. Zbl1072.30006
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