MATHEMATICA BOHEMICA, Vol. 136, No. 1, pp. 51-59, 2011

Invariant approximation for fuzzy
nonexpansive mappings

Ismat Beg, Mujahid Abbas

Ismat Beg, Mujahid Abbas, Centre for Advanced Studies in Mathematics, Lahore University of Management Sciences, 54792 Lahore, Pakistan, e-mail: ibeg@lums.edu.pk; mujahid@lums.edu.pk

Abstract: 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.

Keywords: fuzzy normed space, strictly convex fuzzy normed space, fixed point, fuzzy nonexpansive mapping, fuzzy best approximation, fuzzy Banach mapping

Classification (MSC 2010): 47H10, 47H09, 41A50, 46S40, 54H25, 41A65

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