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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Fixed points of holomorphic maps in Banach spaces
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by T. L. Hayden and T. J. Suffridge PDF
Proc. Amer. Math. Soc. 60 (1976), 95-105 Request permission

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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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 95-105
  • MSC: Primary 47H10; Secondary 58C10
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0417869-3
  • MathSciNet review: 0417869