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Fixed point results for generalized contractions in gauge spaces and applications

Author: M. Frigon
Journal: Proc. Amer. Math. Soc. 128 (2000), 2957-2965
MSC (1991): Primary 47H10, 47N20
Published electronically: June 6, 2000
MathSciNet review: 1769451
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Abstract: In this paper, we present fixed point results for generalized contractions defined on a complete gauge space $\mathbb{E}$. Also, we consider families of generalized contractions $\{f^t : X \to \mathbb{E}\}_{t \in [0,1]}$ where $X \subset \mathbb{E}$ is closed and can have empty interior. We give conditions under which the existence of a fixed point for some $f^{t_0}$ imply the existence of a fixed point for every $f^t$. Finally, we apply those results to infinite systems of first order nonlinear differential equations and to integral equations on the real line.

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Additional Information

M. Frigon
Affiliation: Département de Mathématiques et Statistique, Université de Montréal, C. P. 6128, Succ. Centre-ville, Montréal, Canada H3C 3J7

Received by editor(s): November 19, 1998
Published electronically: June 6, 2000
Additional Notes: This work was partially supported by CRSNG Canada.
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society

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