Neighborhoods of univalent functions

Abstract

For an analytic function f(z) = z + 2Zk0-2akzk m ^ unit disc E conditions are established such that all functions g(z) = z + 2-2bkzk e ^(Z) i.e.X'k^2^\ak ~ *<tl < ^> are m some class of univalent functions in E. For instance, we prove that every g e Nl/4(f) is starlike univalent in E if / is convex univalent.