- 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