Proceedings of the American Mathematical Society

Fixed point results for generalized contractions in gauge spaces and applications

Author(s): M. Frigon
Journal: Proc. Amer. Math. Soc. 128 (2000), 2957-2965.
MSC (1991): Primary 47H10, 47N20
Posted: June 6, 2000
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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

. 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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47H10, 47N20

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

DOI: 10.1090/S0002-9939-00-05838-X
PII: S 0002-9939(00)05838-X
Received by editor(s): November 19, 1998
Posted: June 6, 2000
Additional Notes: This work was partially supported by CRSNG Canada.
Communicated by: David R. Larson
Copyright of article: Copyright 2000, American Mathematical Society

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