A generalization of the Opial's theorem

• Autorzy: Cegielski A.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

nonexpansive operators; asymptotically regular operators; fixed points; weak convergence

PL

punkt stały; słaba zbieżność

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2007
• Tom: Vol. 36, no 3
• Strony: 601--610
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Cegielski A.

• Faculty of Mathematics, Computer Sciences and Econometrics, University of Zielona Gora, ul. Szafrana 4a, 65-516 Zielona Gora, Poland

Bibliografia

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