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International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 653-662

Integral operators of certain univalent functions

Department of Mathematics, University of Papua New Guinea, Box 320, University P.O., , Papua New Guinea

Received 1 October 1984

Copyright © 1985 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A function f, analytic in the unit disc Δ, is said to be in the family Rn(α) if Re{(znf(z))(n+1)/(zn1f(z))(n)}>(n+α)/(n+1) for some α(0α<1) and for all z in Δ, where n ϵ No, No={0,1,2,}. The The class Rn(α) contains the starlike functions of order α for n0 and the convex functions of order α for n1. We study a class of integral operators defined on Rn(α). Finally an argument theorem is proved.