International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 653-662
doi:10.1155/S0161171285000710
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 O. P. Ahuja. 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.
Abstract
A function f, analytic in the unit disc Δ, is said to be in the family Rn(α) if Re{(znf(z))(n+1)/(zn−1f(z))(n)}>(n+α)/(n+1) for some α(0≤α<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 n≥0 and the convex functions of order α for n≥1. We study a class of integral operators defined on Rn(α). Finally an argument theorem is proved.