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Meromorphic starlike univalent functions

Published online by Cambridge University Press:  17 April 2009

V. V. Anh  and
P. D. Tuan
V. V. Anh
Affiliation:
Department of Mathematics, Queensland Institute of Technology, P. O. Box 2434, Brisbane, 4001 Queensland, Australia.
P. D. Tuan
Affiliation:
First Interstate Bank of California, 600 South Spring Street, Los Angeles, CA90014, U.S.A.
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Abstract

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Let B be the class of functions ω(z) regular in |z| < 1 and satisfying ω(0) = 0, |ω(z)|<1 in |z|<1. We denote by P(A, B), −1 ≤ B < A ≤1, the class of functions p(z) = l+p1z+… regular in |z| < 1 and such that p(z) = [1+Aω(z)]/[1+Bω(z)] for some ω(z) ∈ Β. This paper establishes sharp lower and upper bounds on |z| = r<1 for the functional

where p(z) varies in P(A, B). The results are then used to study certain geometric properties of the corresponding class of meromorphic starlike univalent functions

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 30 , Issue 3 , December 1984 , pp. 395 - 410
Copyright
Copyright © Australian Mathematical Society 1984

References

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