Strong Convergence of Averaged Approximants for Lipschitz Pseudocontractive Maps

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Strong convergence theorem for a family of Lipschitz pseudocontractive mappings in a Hilbert space

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. c © 2007 Elsevier Ltd. A...

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Approximate Fixed Point Sequences and Convergence Theorems for Lipschitz Pseudocontractive Maps

Let K be a nonempty closed convex subset of a real Banach space E and T be a Lipschitz pseudocontractive self-map of K with F (T ) := {x ∈ K : Tx = x} 6= ∅. An iterative sequence {xn} is constructed for which ||xn − Txn|| → 0 as n → ∞. If, in addition, K is assumed to be bounded, this conclusion still holds without the requirement that F (T ) 6= ∅. Moreover, if, in addition, E has a uniformly G...

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ژورنال

عنوان ژورنال: Journal of Mathematical Analysis and Applications

سال: 2001

ISSN: 0022-247X

DOI: 10.1006/jmaa.2001.7516