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Invariant approximation for fuzzy nonexpansive mappings

Ismat Beg, Mujahid Abbas (2011)

Mathematica Bohemica

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...

Invariant measures for iterated function systems

Tomasz Szarek (2000)

Annales Polonici Mathematici

A new criterion for the existence of an invariant distribution for Markov operators is presented. Moreover, it is also shown that the unique invariant distribution of an iterated function system is singular with respect to the Hausdorff measure.

Invariant sets and Knaster-Tarski principle

Krzysztof Leśniak (2012)

Open Mathematics

Our aim is to point out the applicability of the Knaster-Tarski fixed point principle to the problem of existence of invariant sets in discrete-time (multivalued) semi-dynamical systems, especially iterated function systems.

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