A generalization of a theorem of Heins

Authors:
James E. Joseph and Myung H. Kwack

Journal:
Proc. Amer. Math. Soc. **128** (2000), 1697-1701

MSC (1991):
Primary 32H99; Secondary 30F99, 32H15

Published electronically:
September 30, 1999

MathSciNet review:
1641112

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the family of holomorphic selfmaps of the unit disk in the complex plane . Heins established the continuity of the functional which assigns to ( denotes the identity map) either (i) the fixed point of or (ii) the limit of its iterations or (iii) if ( represents the boundary of ). Using an Abate extension of the Denjoy-Wolff lemma to strongly convex domains, we extend this result of Heins to selfmaps of strongly convex domains in with boundary.

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Additional Information

**James E. Joseph**

Affiliation:
Department of Mathematics, Howard University, Washington, D. C. 20059

**Myung H. Kwack**

Affiliation:
Department of Mathematics, Howard University, Washington, D. C. 20059

Email:
mkwack@fac.howard.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-05152-7

Keywords:
Iterates,
fixed points,
strongly convex,
horosphere

Received by editor(s):
February 18, 1998

Received by editor(s) in revised form:
July 13, 1998

Published electronically:
September 30, 1999

Dedicated:
In memory of Professor M. Solveig Espelie

Communicated by:
Steven R. Bell

Article copyright:
© Copyright 2000
American Mathematical Society