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Erschienen in:
Open Access 01.12.2006 | Research Article
Implicit predictor-corrector iteration process for finitely many asymptotically (quasi-)nonexpansive mappings
Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2006
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Abstract
We study an implicit predictor-corrector iteration process for finitely many asymptotically quasi-nonexpansive self-mappings on a nonempty closed convex subset of a Banach space
. We derive a necessary and sufficient condition for the strong convergence of this iteration process to a common fixed point of these mappings. In the case
is a uniformly convex Banach space and the mappings are asymptotically nonexpansive, we verify the weak (resp., strong) convergence of this iteration process to a common fixed point of these mappings if Opial's condition is satisfied (resp., one of these mappings is semicompact). Our results improve and extend earlier and recent ones in the literature.
. We derive a necessary and sufficient condition for the strong convergence of this iteration process to a common fixed point of these mappings. In the case
is a uniformly convex Banach space and the mappings are asymptotically nonexpansive, we verify the weak (resp., strong) convergence of this iteration process to a common fixed point of these mappings if Opial's condition is satisfied (resp., one of these mappings is semicompact). Our results improve and extend earlier and recent ones in the literature.