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Certain classes of univalent functions with negative coefficients

Published online by Cambridge University Press:  17 April 2009

V.P. Gupta  and
P.K. Jain
V.P. Gupta
Affiliation:
M.M.H. College, University of Meerut, Ghaziabad, Uttar Pradesh, India;
P.K. Jain
Affiliation:
Department of Mathematics, Hans Raj College, Delhi, India.
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Abstract

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The subclasses S*(α, β) and C*(α, β) of T, the class of analytic and univalent functions of the form have been considered. Sharp results concerning coefficients, distortion of functions belonging to S*(α, β) and C*(α, β) are determined along with a representation formula for the functions in S*(α, β). Furthermore, it is shown that the classes S*(α, β) and C*(α,.β) are closed under arithmetic mean and convex linear combinations.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 3 , June 1976 , pp. 409 - 416
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Schild, A., “On a class of functions schlicht in the unit circle”, Proc. Amer. Math. Soc. 5 (1954), 115–120.CrossRefGoogle Scholar
[2]Silverman, Herb, “Univalent functions with negative coefficients”, Proc. Amer. Math. Soc. 51 (1975), 109–116.CrossRefGoogle Scholar