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On the construction of common fixed points for semigroups of nonlinear mappings in uniformly convex and uniformly smooth Banach spaces

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Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
113--136
Opis fizyczny
Bibliogr. 38 poz.
Twórcy
  • School of Mathematics and Statistics, University of New South Wales Sydney, NSW 2052, Australia
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikator YADDA
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