Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces

By Paul-Emile Maingé. 2007

239 citations recorded by the source corpus.

Abstract The aim of this work is to propose implicit and explicit viscosity-like methods for finding specific common fixed points of infinite countable families of nonexpansive self-mappings in Hilbert spaces. Two numerical approaches to solving this problem are considered: an implicit anchor-like algorithm and a nonimplicit one. The considered methods appear to be of practical interests from the numerical point of view and strong convergence results are proved.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a55e9ceb48699e50ac182058264c33eb5544324e

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In Computational Theory and Mathematics

In Geometry and Topology

In Numerical Analysis

Citations in the corpus

New Methods with Perturbations for Non-Expansive Mappings in Hilbert Spaces (2011, background): “Recently, iterative methods for finding fixed points of non-expansive mappings have received vast investigations due to its extensive applications in a variety of applied areas of inverse problem, partial differential equations, image recovery, and signal processing; see [1-34] and the references th”
An inertial method for solving generalized split feasibility problems over the solution set of monotone variational inclusions (2020, background): “7 ([45]): Let {an} be a sequence of non-negative real numbers satisfying the following: an+1 ≤ (1 − βn)an + σn + γn, n ≥ 1, where {βn} is a sequence in (0, 1) and {σn} is a real sequence.”