Temat: uniformly convex Banach space - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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: 2.

Tytuł:: Implicit random iteration process with errors for asymptotically quasi-nonexpansive in the intermediate sense random operators
Autorzy:: Saluja, G. S.
Powiązania:: https://bibliotekanauki.pl/articles/952767.pdf
Data publikacji:: 2012
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: asymptotically quasi-nonexpansive in the intermediate sense random operator
implicit random iteration process with errors
common random fixed point
strong convergence
separable uniformly convex Banach space
Opis:: In this paper, we give a necessary and sufficient condition for the strong convergence of an implicit random iteration process with errors to a common fixed point for a finite family of asymptotically quasi-nonexpansive in the intermediate sense random operators and also prove some strong convergence theorems using condition (C) and the semi-compact condition for said iteration scheme and operators. The results presented in this paper extend and improve the recent ones obtained by S. Plubtieng, P. Kumam and R. Wangkeeree, and also by the author.
Źródło:: Opuscula Mathematica; 2012, 32, 2; 327-340
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Implicit random iteration process with errors for asymptotically quasi-nonexpansive in the intermediate sense random operators
Autorzy:: Saluja, G. S.
Powiązania:: https://bibliotekanauki.pl/articles/952775.pdf
Data publikacji:: 2012
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: asymptotically quasi-nonexpansive in the intermediate sense random operator
implicit random iteration process with errors
common random fixed point
strong convergence
separable uniformly convex Banach space
Opis:: In this paper, we give a necessary and sufficient condition for the strong convergence of an implicit random iteration process with errors to a common fixed point for a finite family of asymptotically quasi-nonexpansive in the intermediate sense random operators and also prove some strong convergence theorems using condition (C) and the semi-compact condition for said iteration scheme and operators. The results presented in this paper extend and improve the recent ones obtained by S. Plubtieng, P. Kumam and R. Wangkeeree, and also by the author.
Źródło:: Opuscula Mathematica; 2012, 32, 2; 327-340
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

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: 5.

Tytuł:: Fixed points of Lipschitzian semigroups in Banach spaces
Autorzy:: Górnicki, Jarosław
Powiązania:: https://bibliotekanauki.pl/articles/1218872.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Lipschitzian semigroup
fixed point
p-uniformly convex Banach space
Opis:: We prove the following theorem: Let p > 1 and let E be a real p-uniformly convex Banach space, and C a nonempty bounded closed convex subset of E. If $T = {T_s: C → C: s ∈ G = [0,∞)}$ is a Lipschitzian semigroup such that $g = lim inf_{G ∋ α → ∞} inf_{G ∋ δ ≥ 0} 1/α ʃ^α_0 ∥T_{β+δ}∥^p dβ < 1 + c$, where c > 0 is some constant, then there exists x ∈ C such that $T_sx = x$ for all s ∈ G.
Źródło:: Studia Mathematica; 1997, 126, 2; 101-113
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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