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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 paper, we obtain a generalization of a recent result of Tam (2018) which is for iterates of a set-valued paracontracting operators in a finite-dimensional space. Our result in this paper is obtained for operators in a metric space such that every its bounded and closed set is compact. We establish a convergence of inexact iterates of the set-valued operator by taking into account computational errors. [ABSTRACT FROM AUTHOR]

In one of our recent papers, we considered a complete metric space of nonexpansive mappings taking a bounded and closed subset of a complete hyperbolic space into the space so that the boundary of this subset is mapped back into the subset itself. Using the Baire category approach, we proved that most of these mappings possess a unique fixed point which attracts all their iterates. In the present paper, we improve upon this result by showing that the complement of the set of mappings which have a fixed point is not only of the first Baire category, but also is s-porous. [ABSTRACT FROM AUTHOR]

In our joint 2006 paper with Dan Butnariu, it was shown that if all exact orbits of a nonexpansive mapping converge to a fixed point, then this convergence property also holds for all the inexact orbits with summable errors. In the present paper, we establish an analog of this result for the inexact iterates of strict contractions in complete metric spaces with graphs. [ABSTRACT FROM AUTHOR]

We have recently established the existence of a unique fixed point for nonlinear contractive self-mappings of a closed subset of a Banach space, which is not necessarily bounded. In this paper, we extend this result to contractive mappings, which map a closed subset of a Banach space into the space. [ABSTRACT FROM AUTHOR]

The data-compatibility approach to constrained optimization, proposed here, strives to a point that is "close enough" to the solution set and whose target function value is "close enough" to the constrained minimum value. These notions can replace analysis of asymptotic convergence to a solution point of infinite sequences generated by specific algorithms. We consider a problem of minimizing a convex function over the intersection of the fixed point sets of nonexpansive mappings and demostrate the data-compatibility of the Hybrid Subgradient Method (HSM). A string-averaging HSM is obtained as a by-product and relevance to the minimization over disjoint hard and soft constraints sets is discussed. [ABSTRACT FROM AUTHOR]

We introduce a new class of nonlinear contractive mappings in Banach spaces, study their iterates and establish a fixed point theorem for them. [ABSTRACT FROM AUTHOR]

For certain classes of contractive mappings in complete metric spaces, we establish the existence of a fixed point which attracts all inexact orbits. [ABSTRACT FROM AUTHOR]

In our previous work we have shown that if for any initial point there exists a trajectory of a nonexpansive set-valued mapping attracted by a given set, then this property is stable under small perturbations of the mapping. In the present paper we obtain several extensions of this result. [ABSTRACT FROM AUTHOR]

In a recent work, we established the existence of a unique fixed point for nonlinear contractive self-mappings of a bounded and closed set in a Banach space. In the present paper we extend this result to the case of unbounded sets. [ABSTRACT FROM AUTHOR]