Article
MSC:
41A50,
41A65,
46S40,
47H09,
47H10,
54H25 | MR 2807708 | Zbl 1216.47083 | DOI: 10.21136/MB.2011.141449
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Keywords:
fuzzy normed space; strictly convex fuzzy normed space; fixed point; fuzzy nonexpansive mapping; fuzzy best approximation; fuzzy Banach mapping
fuzzy normed space; strictly convex fuzzy normed space; fixed point; fuzzy nonexpansive mapping; fuzzy best approximation; fuzzy Banach mapping
Summary:
We establish results on invariant approximation for fuzzy nonexpansive mappings defined on fuzzy metric spaces. As an application a result on the best approximation as a fixed point in a fuzzy normed space is obtained. We also define the strictly convex fuzzy normed space and obtain a necessary condition for the set of all {$t$-best} approximations to contain a fixed point of arbitrary mappings. A result regarding the existence of an invariant point for a pair of commuting mappings on a fuzzy metric space is proved. Our results extend, generalize and unify various known results in the existing literature.
References:
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