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

• Autorzy: W.M. Kozlowski
• 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 \(T_t\colon C \to C\). Each of \(T_t\) is assumed to be pointwise Lipschitzian, that is, there exists a family of functions \(\alpha_t\colon C \to [0, \infty)\) such that \(\|T_t(x) - T_t (y)\| \leq\alpha_t (x)\|x -y\|\) for \(x, y \in C\). 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

EN

Fixed point; common fixed point; Lipschitzian mapping; pointwise Lipschitzian mapping; semigroup of mappings; asymptotic pointwise nonexpansive mapping; uniformly convex Banach space; uniformly smooth Banach space; Fréchet differentiable norm; weak compactness; fixed point iteration process; Krasnosel'skii-Mann process; Mann process; Ishikawa process

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2012
• Tom: 52
• Numer: 2

Daty

wydano

2012

online

2017-12-19

Twórcy

autor

W.M. Kozlowski

Identyfikatory

DOI

10.14708/cm.v52i2.5331