Viscosity Approximation Methods for Fixed-Points Problems

By Abdellatif Moudafi. 2000

787 citations recorded by the source corpus.

The aim of this work is to propose viscosity approximation methods which amounts to selecting a particular fixed-point of a given nonexpansive self-mapping.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/91f218e2b530f5a2370af7efd3ffa27d6188f51c

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Common zero point for a finite family of inclusion problems of accretive mappings in Banach spaces (2018, result): “The results presented in the paper extend and improve the main results of Moudafi [13], Zegeye et al. [14], López et al. [12], Kim and Xu [15], Rockafellar [9,10] and Cholamjiak [16].”
VISCOSITY APPROXIMATION METHODS FOR NONEXPANSIVE MAPPINGS (2004, methodology): “The viscosity approximation method of selecting a particular fixed point of a given nonexpansive mapping was proposed by Moudafi [6] who proved the strong convergence of both the implicit and explicit methods (4) and (7) in Hilbert spaces.”
Strong convergence theorems for nonexpansive semigroup in Banach spaces (2008, neutral): “(Related results can be found in [7,12–15].”
Solving variational inequalities involving nonexpansive type mappings (2008, neutral): “1, Moudafi [16]) Let C be a nonempty closed convex subset of a Hilbert space H.”
Towards viscosity approximations of hierarchical fixed-point problems (2006, background): “, when Q is a contraction) the problem reduces to the viscosity fixed-point solution introduced in [6] and further developed in [3, 8].”