| On Characterization of Iterative Approximation for Asymptotically Pseudocontractive Mappings |
| Received:September 16, 2002 |
| Key Words:
fixed point asymptotically pseudocontractive mapping uniform Lipschitzian mapping uniform normal structure Banach contraction principle.
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| Fund Project:The Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China, and The Dawn Program Fund in Shanghai. |
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| Abstract: |
| Let C be a nonempty bounded closed convex subset of a Banach space X, and T: C → C be uniformly L-Lipschitzian with L ≥ 1 and asymptotically pseudocontractive with a sequence {kn}?[1, ∞), limn→∞ kn= 1. Fix u ∈ C. For each n ≥ 1, xn is a unique fixed point of the contraction Sn(x) = (1 - tn/(Lkn))u + tn/(Lkn) Tnx ?x ∈ C, where {tn}?[0, 1).Under suitable conditions, the strong convergence of the sequence{xn}to a fixed point of T is characterized. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2005.02.009 |
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