Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H10, 58C10

Retrieve articles in all journals with MSC: 47H10, 58C10

Additional Information

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