## 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