Abstract
We introduce extensions to uniform spaces of some classical theorems of nonlinear analysis, whose original setting corresponded to complete metric spaces. Our results are based on a condition for a filter base, on uniform spaces, to have a nonempty intersection. Using this condition, we prove the existence of maximal elements for a given preordering, the existence of fixed points for multivalued functions, and related issues. Well-known results by Nadler and Saint-Raymond, in the setting of metric spaces, are also extended to the uniform space scenario.
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Acknowledgements
First of all, we are very grateful for an anonymous referee, because their valuable suggestions allowed us to improve the content of this paper. This research was partially supported by Chilean Council for Scientific and Technological Research, under Grant No. FONDECYT 1200525.
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Fierro, R. A condition on uniform spaces for the existence of maximal elements and fixed points. J. Fixed Point Theory Appl. 24, 59 (2022). https://doi.org/10.1007/s11784-022-00976-3
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DOI: https://doi.org/10.1007/s11784-022-00976-3