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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 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.

Iterative solution of nonlinear equations of the pseudo-monotone type in Banach spaces

A. M. Saddeek, Sayed A. Ahmed (2008)

Archivum Mathematicum

The weak convergence of the iterative generated by J ( u n + 1 - u n ) = τ ( F u n - J u n ) , n ≥ 0 , ( 0 < τ = min { 1 , 1 λ } ) to a coincidence point of the mappings F , J : V → V ☆ is investigated, where V is a real reflexive Banach space and V ☆ its dual (assuming that V ☆ is strictly convex). The basic assumptions are that J is the duality mapping, J - F is demiclosed at 0 , coercive, potential and bounded and that there exists a non-negative real valued function r ( u , η ) such that sup u , η ∈ V { r ( u , η ) } = λ < ∞ ...

Kannan-type cyclic contraction results in 2 -Menger space

Binayak S. Choudhury, Samir Kumar BHANDARI (2016)

Mathematica Bohemica

In this paper we establish Kannan-type cyclic contraction results in probabilistic 2-metric spaces. We use two different types of t -norm in our theorems. In our first theorem we use a Hadzic-type t -norm. We use the minimum t -norm in our second theorem. We prove our second theorem by different arguments than the first theorem. A control function is used in our second theorem. These results generalize some existing results in probabilistic 2-metric spaces. Our results are illustrated with an example....

Large games with only small players and finite strategy sets

Andrzej Wieczorek (2004)

Applicationes Mathematicae

Large games of kind considered in the present paper (LSF-games) directly generalize the usual concept of n-matrix games; the notion is related to games with a continuum of players and anonymous games with finitely many types of players, finitely many available actions and distribution dependent payoffs; however, there is no need to introduce a distribution on the set of types. Relevant features of equilibrium distributions are studied by means of fixed point, nonlinear complementarity and constrained...

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