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On mean p-valent functions in an ellipse

Published online by Cambridge University Press:  14 November 2011

M. M. Elhosh
M. M. Elhosh
Affiliation:
Pure Mathematics Department, University College of Wales, Aberystwyth
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Synopsis

Modulus and coefficient bounds for functions mean p-valent in the interior of an ellipse, analogous to known bounds for the unit disc, are established in this paper.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 1-2 , 1982 , pp. 1 - 11
Copyright
Copyright © Royal Society of Edinburgh 1982

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References

1Ahlfors, L. V.. Complex Analysis (New York: McGraw-Hill, 1953).Google Scholar
2Hayman, W. K.. Multivalent Functions (Cambridge: Cambridge University Press, 1958).Google Scholar
3Nehari, Z.. Conformal Mapping (New York: McGraw-Hill, 1952).Google Scholar
4Pommerenke, Ch.. Über die Mittelwerte und Koeffizienten Multivalenter Functionen. Math. Ann. 145 (1962), 285–296.Google Scholar
5Royster, W. C.. Coefficient problems for functions regular in an ellipse. Duke Math. J. 26 (1959), 361–371.CrossRefGoogle Scholar
6Szegö, G.. Orthogonal polynomials. Amer. Math. Soc. Colloq. Publ. 23 (1939).Google Scholar
7Holland, F. and Twomey, J. B.. On Hardy classes and the area function. J. London Math. Soc. 17 (1978), 275–283.CrossRefGoogle Scholar