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We study the space of all continuous and increasing self-mappings of a real interval [a, b], where a < b are real numbers, equipped with the topology of uniform convergence. We show, in particular, that most such functions have infinitely many different fixed points. [ABSTRACT FROM AUTHOR]

In this paper, we study the method of cyclic projections for inconsistent convex feasibility problems in a Hilbert space under the presence of computational errors. We show that our algorithm generates a good approximate solution, if computational errors are bounded from above by a small positive constant. Our main goal is, for a known computational error, to find out what approximate solution can be obtained and how many iterates one needs for this. [ABSTRACT FROM AUTHOR]

Given a nonexpansive mapping which maps a closed subset of a complete metric space into the space, we study the convergence of its inexact iterates to its fixed point set in the case where the errors are nonsummable. Previous results in this direction concerned nonexpansive self-mappings of the complete metric space and inexact iterates with summable errors. [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 this paper, we study three fixed point problems. The first one is a fixed point problem with a set-valued mapping, while the second and third problems are convex feasibility problems with infinitely many constraints solved by the subgradient projection algorithm. We show that an approximate solution is reached after a finite number of iterations under the presence of computational errors. [ABSTRACT FROM AUTHOR]

We first study the asymptotic behavior of infinite products of nonexpansive selfmappings of a star-shaped complete metric space which is not necessarily bounded. Using the notion of contractivity and the Baire category approach, we show that a typical (generic) sequence of nonexpansive mappings is contractive and generates infinite products which have the same asymptotic behavior. This result is then applied to certain classes of nonexpansive set-valued self-mappings of a closed and star-shaped subset of a Banach space. It is shown that in these classes most (in the sense of Baire category) mappings are contractive. In particular, we show that this fact is true for a certain class of compact-valued mappings. It follows that a generic mapping in this class has a fixed point. [ABSTRACT FROM AUTHOR]