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Abstrakty
Let C be a bounded, closed, convex subset of a uniformly convex and uniformly smooth Banach space X. We investigate the weak convergence of the generalized Krasnosel'skii-Mann and Ishikawa iteration processes to common fixed points of semigroups of nonlinear mappings Tt: C → C. Each of Tt: is assumed to be pointwise Lipschitzian, that is, there exists a family of functions αt: C → [0, ∞) such that ||Tt(x) — Tt(y)\\ ≤ αt:(x) || - y|| for x,y € C. The paper demonstrates how the weak compactness of C plays an essential role in proving the weak convergence of these processes to common fixed points.
Słowa kluczowe
fixed point
common fixed point
Lipschitzian mapping
pointwise Lipschitzian mapping semigroup of mappings
asymptotic pointwise no-nexpansive mapping
uniformly convex Banach space
uniformly smooth Banach spaces
Frechet differentiable norm
weak compactness
fixed point iteration
process Krasnosel'skii-Mann process
Mann process
Ishikawa process
Wydawca
Czasopismo
Rocznik
Tom
Strony
113--136
Opis fizyczny
Bibliogr. 38 poz.
Twórcy
autor
- School of Mathematics and Statistics, University of New South Wales Sydney, NSW 2052, Australia
Bibliografia
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Bibliografia
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