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On p–valent starlike functions with reference to the Bernardi integral operator

Published online by Cambridge University Press:  17 April 2009

Vinod Kumar  and
S.L. Shukla
Vinod Kumar
Affiliation:
Dr V. Kumar, Department of Mathematics, Christ Church College, Kanpur–208001, India.
S.L. Shukla
Affiliation:
Dr S.L. Shukla, Department of Mathematics, Janta College, Bakewar, Etawah–206124, India.
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Abstract

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Let (A, B) denote the class of certain p-valent starlike functions. Recently G. Lakshma Reddy and K.S. Padmanabhan [Bull. Austral. Math. Soc. 25 (1982), 387–396] have shown that the function g defined by

belongs to the class (A, B) if f ∈ (A, B). The technique used by them fails when c is any positive real number. In this paper, by employing a more powerful technique, we improve their result to the case when c is any real number such that c ≥ −p(1+A)/(1+B).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 30 , Issue 1 , August 1984 , pp. 37 - 43
Copyright
Copyright © Australian Mathematical Society 1984

References

[1;]Bernardi, S.D., “Convex and starlike univalent functions”, Trans. Amer. Math. Soc. 135 (1969), 429–446.CrossRefGoogle Scholar
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[4]Kumar, Vinod and Shukla, S.L., “Bazilevič integral operators”, Rend. Mat. 3 (1983).Google Scholar
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[6]Reddy, G. Lakshma and Padmanabhan, K.S., “On analytic functions with reference to Bernardi integral operator”. Bull. Austral. Math. Soc. 25 (1982), 387–396.Google Scholar