Locally univalent functions and coefficient distortions

Herbert Silverman, Evelyn Marie Silvia and D. N. Telage

Vol. 77 (1978), No. 2, 533–539

DOI: 10.2140/pjm.1978.77.533

Abstract

We look at functions f(z) = z + ∑ _n=2^∞a_nzⁿ 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.

Mathematical Subject Classification 2000

Primary: 30C45

Milestones

Received: 15 July 1977

Revised: 16 November 1977

Published: 1 August 1978