Autor: Kozlowski, W. - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Artykuł

Skocz do pozycji: 2.

Tytuł:: On the construction of common fixed points for semigroups of nonlinear mappings in uniformly convex and uniformly smooth Banach spaces
Autorzy:: Kozlowski, W.M.
Powiązania:: https://bibliotekanauki.pl/articles/746293.pdf
Data publikacji:: 2012
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: common fixed point
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
Opis:: 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.
Źródło:: Commentationes Mathematicae; 2012, 52, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Strong convergence of implicit iteration processes for nonexpansive semigroups in Banach spaces
Autorzy:: Kozlowski, W.M.
Powiązania:: https://bibliotekanauki.pl/articles/746461.pdf
Data publikacji:: 2014
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: fixed point
nonexpansive mapping
nonexpansive semigroup
fixed point iteration process
implicit iterative process
strong convergence
uniformly convex Banach space
Opis:: Let $C$ be a convex compact subset of a uniformly convex Banach space. Let $\{T_t\}_{t \geq0}$ be a strongly-continuous nonexpansive semigroup on $C$. Consider the iterative process defined by the sequence of equations $$x_{k+1} =c_k T_{t_{k+1}}(x_{k+1})+(1-c_k)x_k.$$ We prove that, under certain conditions on $\{c_k\}$ and $\{t_k\}$, the sequence $\{x_k\}_{n=1}^\infty$ converges strongly to a common fixed point of the semigroup $\{T_t\}_{t \geq0}$. There are known results on convergence of such iterative processes for nonexpansive semigroups in Hilbert spaces and Banach spaces with the Opial property, and also weak convergence results in Banach spaces that are simultaneously uniformly convex and uniformly smooth. In this paper, we do not assume the Opial property or uniform smoothness of the norm.
Źródło:: Commentationes Mathematicae; 2014, 54, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Artykuł

Skocz do pozycji: 5.

Artykuł

Skocz do pozycji: 6.

Tytuł:: On Nonlinear Differential Equations in Generalized Musielak-Orlicz Spaces
Autorzy:: Kozlowski, W.M.
Powiązania:: https://bibliotekanauki.pl/articles/744903.pdf
Data publikacji:: 2013
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: ordinary differential equation, nonlinear equation, Cauchy problem, initial value problem, fixed point, nonexpansive mapping, modular function space, Orlicz space, Musielak-Orlicz space, convex modular
Opis:: We consider ordinary differential equations $u'(t)+(I-T)u(t)=0$, where an unknown function takes its values in a given modular function space being a generalization of Musielak-Orlicz spaces, and $T$ is nonlinear mapping which is nonexpansive in the modular sense. We demonstrate that under certain natural assumptions the Cauchy problem related to this equation can be solved. We also show a process for the construction of such a solution. This result is then linked to the recent results of the fixed point theory in modular function spaces.
Źródło:: Commentationes Mathematicae; 2013, 53, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Informacja