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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Fixed points of holomorphic maps in Banach spaces

Authors: T. L. Hayden and T. J. Suffridge
Journal: Proc. Amer. Math. Soc. 60 (1976), 95-105
MSC: Primary 47H10; Secondary 58C10
MathSciNet review: 0417869
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Abstract: This paper is concerned with the problem of existence of fixed points of continuous maps of the closed unit ball of a complex Banach space into itself which are holomorphic on the open unit ball. We show that if the Banach space is separable and reflexive and F is the map in question that for a.e. $ \theta $ in $ [0,2\pi ]$ the map $ {e^{i\theta }}$ F has a fixed point. This result does not hold in general; hence, additional conditions are imposed which insure the existence of fixed points in every Banach space. Fixed points of some linear fractional maps are explicitly computed.

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Keywords: Fixed points, holomorphic mappings, invariant metric
Article copyright: © Copyright 1976 American Mathematical Society