Fixed point results for generalized contractions in gauge spaces and applications
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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.References
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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
- Email: frigon@dms.umontreal.ca
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2957-2965
- MSC (1991): Primary 47H10, 47N20
- DOI: https://doi.org/10.1090/S0002-9939-00-05838-X
- MathSciNet review: 1769451