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New strong convergence theorems for nonexpansive nonself-mappings without boundary conditions. (English) Zbl 1155.65345

Summary: The aim of this work is to establish the strong convergence of explicit viscosity-like methods for a nonexpansive nonself-mapping without boundary conditions defined in a Banach space. This gets rid of the restriction and dependence on the implicit anchor-like continuous path \(x_t\) in the existing literature.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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