Related papers: Iterative schemes for computing fixed points of no…
In this paper we investigate iteration of maps on lattices and the corresponding polynomial-like iterative equation. Since a lattice need not have a metric space structure, neither the Schauder fixed point theorem nor the Banach fixed point…
Recently, versions of neural networks with infinite-dimensional affine operators inside the computational units (``neural operator'' networks) have been applied to learn solutions to differential equations. To enable practical computations,…
Banach's fixed point theorem in linear n-normed space is being developed. Also, we present several theorems on fixed points in linear n-normed space.
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
The main purpose of this paper is to extend some fixed point results for single valued $b$-enriched nonexpansive mappings to the case of multivalued mappings. To this end, we introduce *-$b$-enriched nonexpansive mappings, as a…
The purpose of this article is to study the existence of a coincidence point for two mappings defined on a nonempty set and taking values on a Banach space using the fixed point theory for nonexpansive mappings. Moreover, this type of…
The question of extension of locally defined maps to the entire space arises in many problems of analysis (e.g., local linearization of functional equations). A known classical method of extension of smooth local maps on Banach spaces uses…
We consider a class of generalized nonexpansive mappings introduced by Karapinar [5] and seen as a generalization of Suzuki (C)-condition. We prove some weak and strong convergence theorems for approximating fixed points of such mappings…
We investigate the rate of convergence of the iterates of an n-dimensional quasiregular mapping within the basin of attraction of a fixed point of high local index. A key tool is a refinement of a result that gives bounds on the distortion…
First we prove that if a separable Banach space $X$ contains an isometric copy of an infinite-dimensional space $A(S)$ of affine continuous functions on a Choquet simplex $S$, then its dual $X^*$ lacks the weak$^*$ fixed point property for…
Some known fixed point theorems for nonexpansive mappings in metric spaces are extended here to the case of primitive uniform spaces. The reasoning presented in the proofs seems to be a natural way to obtain other general results.
In this paper, two generalized algorithms for solving the variational inequality problem in Banach spaces are proposed. Then the strong convergence of the sequences generated by these algorithms will be proved under the suitable conditions.…
We consider a Banach space, which comes naturally from c0 and it appears in the literature, and we prove that this space has the fixed point property for non-expansive mappings.
In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…
We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the Method of Alternating Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection Algorithm…
This paper proposes a unified framework for the investigation of constrained learning theory in reflexive Banach spaces of features via regularized empirical risk minimization. The focus is placed on Tikhonov-like regularization with…
We introduce the notion of firm non-expansive mapping in weak metric spaces, extending previous work for Banach spaces and certain geodesic spaces. We prove that, for firm non-expansive mappings, the minimal displacement, the linear rate of…
We present a rigorous numerical scheme for the approximation of the linear response of the invariant density of a map with an indifferent fixed point, with explicit and computed estimates for the error and all the involved constants.
This paper analyzes the convergence for a large class of Riemannian stochastic approximation (SA) schemes, which aim at tackling stochastic optimization problems. In particular, the recursions we study use either the exponential map of the…
We study the computational difficulty of the problem of finding fixed points of nonexpansive mappings in uniformly convex Banach spaces. We show that the fixed point sets of computable nonexpansive self-maps of a nonempty, computably weakly…