- Tytuł:
- A generalization of the Opials theorem
- Autorzy:
- Cegielski, A.
- Powiązania:
- https://bibliotekanauki.pl/articles/970267.pdf
- Data publikacji:
- 2007
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
punkt stały
słaba zbieżność
nonexpansive operators
asymptotically regular operators
fixed points
weak convergence - Opis:
- Opial presented in 1967 a theorem, which can be applied in order to prove the weak convergence of sequences (xk) in a Hilbert space, generated by iterative schemes of the form xk+1= Uxk for a nonexpansive and asymptotically regular operator U with nonempty Fix U. Several iterative schemes have, however, the form xk+i1 = UkXk, where (Uk) is a sequence of operators with a common fixed point. We show that under some conditions on the sequence (Uk) the sequence (xk) converges weakly to a common fixed point of operators Uk- We show also that the Opial's theorem and the Krasnoselskii-Mann theorem are the corollaries descending from the obtained results. Finally, we present some applications of the results to the convex feasibility problems.
- Źródło:
-
Control and Cybernetics; 2007, 36, 3; 601-610
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł