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In the present paper, we obtain three results on the existence of a fixed point for nonexpansive mappings. Two of them are generalizations of the result for F-contraction, while third one is a generalization of a recent result for set-valued contractions. [ABSTRACT FROM AUTHOR]

In this work, we study an iterative process induced by a contractive type set-valued mapping in a complete metric space and show its convergence, taking into account computational errors. [ABSTRACT FROM AUTHOR]

In this work we show that if iterates of a nonexpansive self-mapping of a complete metric with a graph converge uniformly on a subset of the space, then this convergence is stable under the presence of small computational errors. [ABSTRACT FROM AUTHOR]

In this paper, we study a feasibility problem with infinitely many sets in a metric space. We present a novel algorithm and analyze its convergence. The algorithms used for the feasibility problem in the literature work for finite collections of sets and cannot be applied if the collection of sets is infinite. The main feature of these algorithms is that, for iterative steps, we need to calculate the values of all the operators belonging to our family of maps and even their sums with weighted coefficients. This is impossible if the family of maps is not finite. In the present paper, we introduce a new algorithm for solving feasibility problems with infinite families of sets and study its convergence. It turns out that our results hold for feasibility problems in a general metric space. [ABSTRACT FROM AUTHOR]

We analyze the asymptotic behavior of infinite products of non-linear operators which take a non-empty, closed subset of a complete metric space into the space, taking into account summable computational errors. Our results can be applied in methods for solving convex feasibility and optimization problems. [ABSTRACT FROM AUTHOR]

In our 2006 paper with D. Butnariu, it was shown that the convergence of iterates of a nonexpansive self-mapping of a complete metric space is stable in the presence of summable computational errors. In the present paper, we establish such results for monotone nonexpansive mappings. [ABSTRACT FROM AUTHOR]

We study the behavior of inexact products of uniformly continuous self-mappings of a complete metric space that is uniformly continuous and bounded on bounded sets. It is shown that previously established convergence theorems for products of non-expansive mappings continue to hold even under the presence of computational errors. [ABSTRACT FROM AUTHOR]

In this work, we obtain a weak version of the turnpike property of trajectories of perturbed discrete disperse dynamical systems, which have a prototype in mathematical economics. [ABSTRACT FROM AUTHOR]