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Strong convergence of an iterative method with perturbed mappings for nonexpansive and accretive operators. (English) Zbl 1140.47050
Summary: A new iterative method for finding a zero of \(m\)-accretive operators is proposed. This method, involving a so-called perturbed mapping, provides a way to construct sunny nonexpansive retractions. Several strong convergence theorems for this method are established in a Banach space that is either uniformly smooth or reflexive with a weakly continuous duality map.

MSC:
47J25 Iterative procedures involving nonlinear operators
47H06 Nonlinear accretive operators, dissipative operators, etc.
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
47H14 Perturbations of nonlinear operators
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