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An area theorem for bounded univalent functions

Published online by Cambridge University Press:  24 October 2008

Pran Nath Chichra
Affiliation:
Punjabi University, Patiala, India

Extract

Let f(z) be regular and univalent in |z| < 1 with a power series expansion

Then it is proved in (2) that

where z1 and z2 are points in |z| < 1.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Hayman, W. K.Miltivalent functions (Cambridge University Press, 1958).Google Scholar
(2)Ladegast, K.Beitrage Zur Theorie der Schlichten Funktionen. Math. Z. 58 (1953).CrossRefGoogle Scholar
(3)Nehari, Z.Conformal mapping (McGraw-Hill, 1952).Google Scholar
(4)Nehari, Z.The Schwarzian derivative and Schlicht functions. Bull. Atner. Math. Soc. 55 (1949).Google Scholar
(5)Singh, V.Grunsky inequalities and coefficients of bounded Schlicht functions. Ann. Acad. Sci. Fenn. Ser. A I, 310 (1962).Google Scholar