Geodesic
Invariant approximation for fuzzy nonexpansive mappings
Mathematica Bohemica, Tome 136 (2011) no. 1, pp. 51-59

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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.
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.
DOI : 10.21136/MB.2011.141449
Classification : 41A50, 41A65, 46S40, 47H09, 47H10, 54H25
Keywords: fuzzy normed space; strictly convex fuzzy normed space; fixed point; fuzzy nonexpansive mapping; fuzzy best approximation; fuzzy Banach mapping 
Beg, Ismat; Abbas, Mujahid. Invariant approximation for fuzzy nonexpansive mappings. Mathematica Bohemica, Tome 136 (2011) no. 1, pp. 51-59. doi: 10.21136/MB.2011.141449
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