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On Nunokawa's conjecture for multivalent functions

Published online by Cambridge University Press:  17 April 2009

Shigeyoshi Owa
Shigeyoshi Owa
Affiliation:
Department of MathematicsKinki UniversityHigashi-Osaka, Osaka 577Japan
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Abstract

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The object of this paper is to prove a conjecture given recently by Nunokawa that if f(z) ∈ Α(p) satisfies Re{1 + zf″(z)/f′(z)} < p + 1/2 in the unit disk U, then f(z) is p-valently starlike in U.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 2 , April 1990 , pp. 301 - 305
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Jack, I.S., ‘Functions starlike and convex of order α’, J. London Math. Soc. 3 (1971), 469–474.CrossRefGoogle Scholar
[2]Miller, S.S. and Mocanu, P.T., ‘Second order differential inequalities in the complex plane“, J. Math. Anal. Appl. 65 (1978), 289–305.CrossRefGoogle Scholar
[3]Nunokawa, M., ‘On the multivalent functions’, Indian J. Pure Appl. Math. 20 (1989), 577–582.Google Scholar
[4]Singh, R. and Singh, S., ‘Some sufficient conditions for univalence and starlikeness’, Colloq. Math. 47 (1982), 309–314.CrossRefGoogle Scholar