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Perturbation techniques for nonexpansive mappings with applications. (English) Zbl 1163.47306

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:

47H14 Perturbations of nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J05 Equations involving nonlinear operators (general)
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