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Zbl 1145.47305
Zhang, Qing-Bang; Cheng, Cao-Zong
Strong convergence theorem for a family of Lipschitz pseudocontractive mappings in a Hilbert space. (English)
[J] Math. Comput. Modelling 48, No. 3-4, 480-485 (2008). ISSN 0895-7177

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.

MSC 2000:: *47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47J25 Methods for solving nonlinear operator equations (general)
65J15 Equations with nonlinear operators (numerical methods)

Keywords: Lipschitz pseudocontractive mapping; modified Ishikawa iterative process; strong convergence

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Zentralblatt MATH Berlin [Germany]