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A generalization of a theorem of Heins |
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| Authors: | James E. Joseph Myung H. Kwack |
| Affiliation: | Department of Mathematics, Howard University, Washington, D. C. 20059 Myung H. Kwack ; Department of Mathematics, Howard University, Washington, D. C. 20059 |
| 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. |
| Keywords: | Iterates fixed points strongly convex horosphere |
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