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

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.