# 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

top- Ahlfors, L. V., Conformal Invariants: Topics in Geometric Function Theory, McGraw-Hill Book Company, New York-Düsseldorf-Johannesburg, 1973.
- Bernstein, S. N., Sur la limitation des dérivées des polynomes, C. R. Math. Acad. Sci. Paris 190 (1930), 338-340. Zbl56.0301.02
- Boas, Jr., R. P., Entire Functions, Academic Press, New York, 1954.
- Carathéodory, C., Conformal Representation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 28, Cambridge University Press, Cambridge, 1963. Zbl58.0354.14
- 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