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On the Monotonicity of Certain Functionals in the Theory of Analytic Functions

Published online by Cambridge University Press:  20 November 2018

Q.I. Rahman
Q.I. Rahman*
Affiliation:
Université de Montréal
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Let f(z) be a function regular for | z | < R, and denote by L(r) the length of the curve Γ onto which the circle | z | = r is mapped by f(z), i. e.

If Dr is the image of | z | ≤ r on the Riemann surface of f(z) then its area S(r) is given by

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 5 , December 1967 , pp. 723 - 729
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Biernacki, M. and Krzyz, J., On the monotonity of certain functionals in the theory of analytic functions. Annales Universitatis MariaeCurie-Skłrodowska, Lublin (Poland). Vol. IX (1955), pp. 135-145.Google Scholar
2. Titchmarsh, E. C., Theory of Functions, Oxford (1933).Google Scholar