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Certain integrals for classes of p-valent meromorphic functions

Published online by Cambridge University Press:  17 April 2009

Vinod Kumar  and
S.L. Shukla
Vinod Kumar
Affiliation:
Department of Mathematics, Janta College, Bakewar 206124, Etawah (U.P.), India.
S.L. Shukla
Affiliation:
Department of Mathematics, Janta College, Bakewar 206124, Etawah (U.P.), India.
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Abstract

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In this paper we introduce two classes, namely Γp(m, M) and Σp(m, M), of functions

regular and p-valent in D − {0} where D = {z : |z| < 1}. We show that, for suitable choices of real constants α, β and γ, the integral operators of the form

map into , where is the class of p-valent meromorphically starlike functions of order ρ, 0 ≤ ρ < 1. For the classes Γp(m, M) and Σp(m, M), we obtain class preserving integral operators of the form

with suitable restrictions on real constants α and γ.

Our results generalize almost all known results obtained so far in this direction.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1982 , pp. 85 - 97
Copyright
Copyright © Australian Mathematical Society 1982

References

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