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Given a convex objective function on a Banach space, which is Lipschitz on bounded sets, we consider the class of regular vector fields introduced in our previous work on descent methods. We analyze the behaviour of the values of the objective function for two iterative processes generated by a regular vector field in the presence of computational errors and show that if the computational errors tend to zero, then the values of the objective function converge to its infimum. [ABSTRACT FROM AUTHOR]

In our 2014 work with M. Gabour, we introduced a metric space of generalized nonexpansive self-mappings of bounded and closed subsets of a Banach space and studied, using the Baire category approach, the asymptotic behavior of iterates of a generic operator belonging to this class. In the definition of a generalized nonexpansive mapping the norm is replaced by a general function which can be symmetric as a particular case. In this paper, we prove the convergence of infinite products of generalized nonexpansive self-mappings to a common fixed point in a generic setting. [ABSTRACT FROM AUTHOR]

The notion of porosity is well known in Optimization and Nonlinear Analysis. Its importance is brought out by the fact that the complement of a ɑ-porous subset of a complete pseudo-metric space is a residual set, while the existence of the latter is essential in many problems which apply the generic approach. Thus, under certain circumstances, some refinements of known results can be achieved by looking for porous sets. In 2001 Gabour, Reich and Zaslavski developed certain generic methods for solving stochastic feasibility problems. This topic was further investigated in 2021 by Barshad, Reich and Zaslavski, who provided more general results in the case of unbounded sets. In the present paper we introduce and examine new generic methods that deal with the aforesaid problems, in which, in contrast with previous studies, we consider sigma-porous sets instead of meager ones. [ABSTRACT FROM AUTHOR]

Given a convex objective function on a Banach space which is Lipschitz on bounded sets and satisfies a coercivity growth condition, we prove two convergence results for a gradient-type method, generated by a regular vector field, under the presence of computational errors. We show that if the computational errors are small enough, then the values of the objective function become close to its infimum. [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]

Given a convex objective function on a Banach space which is Lipschitz on bounded sets and satisfies a coercivity growth condition, we consider an iterative process generated by a regular vector field, under the presence of computational errors. We show that if the computational errors are small enough, then the values of the objective function become close to its infimum. [ABSTRACT FROM AUTHOR]

Given a Lipschitz convex and coercive objective function on a Banach space, we revisit the class of regular vector fields introduced in our previous work on descent methods. Taking into account computational errors, we study the behaviour of the values of the objective function for the process generated by a regular vector field and show that if the computational errors are small enough, then the values of the objective function become close to its infimum. [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]

Given a Lipschitz and convex objective function of an unconstrained optimization problem, defined on a Banach space, we revisit the class of regular vector fields which was introduced in our previous work on descent methods. We study, in particular, the asymptotic behavior of the sequence of values of the objective function for a certain inexact process generated by a regular vector field when the sequence of computational errors converges to zero and show that this sequence of values converges to the infimum of the given objective function of the unconstrained optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of inexact infinite products of nonexpansive mappings, which take a nonempty, closed subset of a complete metric space into the space under the presence of summable errors, and generalize the known results in the literature for nonexpansive selfmappings on the complete metric space. [ABSTRACT FROM AUTHOR]

In this paper we study the convergence of inexact iterates of nonexpansive mappings which take a nonempty, closed subset of a complete metric space into the space, under the presence of summable errors, and generalize the known results in the literature for nonexpansive self-mappings of the complete metric space. [ABSTRACT FROM AUTHOR]

We study monotone nonexpansive self-mappings of a closed and convex cone in an ordered Banach space with particular emphasis on the asymptotic behavior of their inexact iterates. [ABSTRACT FROM AUTHOR]

In our recent work we have introduced and studied a notion of a generalized nonexpansive mapping. In the definition of this notion the norm has been replaced by a general function satisfying certain conditions. For this new class of mappings, we have established the existence of unique fixed points and the convergence of iterates. In the present paper we construct an example of a generalized nonexpansive self-mapping of a bounded, closed and convex set in a Hilbert space, which is not nonexpansive in the classical sense. [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]