Locally univalent functions and coefficient distortions

Abstract

We look at functions f(z) = z + =2 a n z n satisfying: n=2 n \a n \ > 1 and determine conditions for which the arguments of the coefficients may vary without affecting the univalence of the function. A bound on the radius of starlikeness for the convolution of functions taken from the closed convex hull of convex functions and a special subclass of starlike functions is also obtained.