Vol. 77, No. 2, 1978

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Locally univalent functions and coefficient distortions

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

Vol. 77 (1978), No. 2, 533–539
Abstract

We look at functions f(z) = z + n=2anzn satisfying n=2n|an| > 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
Authors
Herbert Silverman
Evelyn Marie Silvia
D. N. Telage