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Jakubowski starlike integral operators

Part of: Geometric function theory

Published online by Cambridge University Press:  09 April 2009

Vinod Kumar  and
S. L. Shukla
Vinod Kumar
Affiliation:
Department of Mathematics Feroze Gandhi CollegeRae Bareli 229001, India
S. L. Shukla
Affiliation:
Department of Mathematics Janta CollegeBakewar, Etawah 206124, India
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Abstract

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Let S(m, M) be the set of functions regular and satisfying │zf′(z)/f(z) – m│< M in │z│ <1, where│m –│ <M;≦ m; and let S*(p) be the set of starlike functions of order p, 0≦ p <1. In this paper we obtain integral operators which map S(m, M) into S(mM) and S* (p) × S(mM) into S*(p). Our results improve and generalize many recent results.

Keywords

univalentstarlikeclose-to-convex.

MSC classification

Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 1 , August 1984 , pp. 117 - 127
Copyright
Copyright © Australian Mathematical Society 1984

References

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