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Coefficient estimates for starlike functions

Published online by Cambridge University Press:  17 April 2009

M.L. Mogra  and
O.P. Juneja
M.L. Mogra
Affiliation:
Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur, India.
O.P. Juneja
Affiliation:
Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur, India.
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Abstract

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Let (α β) denote the class of functions

analytic in the unit disc Δ ≡{z: |z| < 1} and satisfying

for some α, β (0 ≤ α < 1, 0 < β ≤ 1) and for all z ∈ Δ. In the present paper, sharp coefficient estimates for functions in (α, β) have been obtained. The results thus obtained not only generalize the corresponding results of Thomas H. MacGregor (Michigan Math. J. 10 (1963), 277–281), A.V. Boyd (Proc. Amer. Math. Soc. 17 (1966), 1016–1018) and others, but also give rise to analogous results for various other subclasses of starlike functions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 3 , June 1977 , pp. 415 - 425
Copyright
Copyright © Australian Mathematical Society 1977

References

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