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A fixed point theorem for α-condensing maps on a sphere*

Published online by Cambridge University Press:  14 November 2011

Paul Massatt
Paul Massatt
Affiliation:
Department of Mathematics, University of Oklahoma at Norman, U.S.A
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Synopsis

This paper shows that if S is a sphere in a Banach space and f: S → S is an α-contraction, then f has a fixed point. The paper generalizes a result of R. D. Nussbaum which holds for α-contractions only. The proof uses the Browder nonrepulsive fixed point theorem and is motivated by recent work of M. Martelli and G. D. Cooperman.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 3-4 , 1983 , pp. 323 - 329
Copyright
Copyright © Royal Society of Edinburgh 1983

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