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Strong convergence theorem for a family of Lipschitz pseudocontractive mappings in a Hilbert space. (English) Zbl 1145.47305
Summary: A extension of Nakajo and Takahashi’s modification of Mann’s iterative process to the Ishikawa iterative process is given. The strong convergence of a modified Ishikawa iterative scheme to a common fixed point of a finite family of Lipschitz pseudocontractive self-mappings on a closed convex subset of a Hilbert space is proved. Our theorem extends several known results.

47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47J25Iterative procedures (nonlinear operator equations)
65J15Equations with nonlinear operators (numerical methods)
Full Text: DOI
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