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Zbl 1163.47306
Lopez, Genaro; Martin, Victoria; Xu, Hong-Kun
(López Acedo, Genaro)
Perturbation techniques for nonexpansive mappings with applications. (English)
[J] Nonlinear Anal., Real World Appl. 10, No. 4, 2369-2383 (2009). ISSN 1468-1218

Summary: Perturbation techniques for nonexpansive mappings are studied. An iterative algorithm involving perturbed mappings in a Banach space is proposed and proved to be strongly convergent to a fixed point of the original mapping. These techniques are applied to solve the split feasibility problem and the multiple-sets split feasibility problem, and to find zeros of accretive operators.

MSC 2000:: *47H14 Perturbations of nonlinear operators
47H09 Mappings defined by "shrinking" properties
47J05 Equations involving nonlinear operators (general)

Keywords: split feasibility problem; multiple-sets split feasibility problem; projection; nonexpansive mapping; sunny nonexpansive retraction; fixed point; accretive operator; iterative algorithm; perturbation; duality map

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