International Journal of Functional Analysis, Operator Theory and Applications
Volume 1, Issue 1, Pages 9 - 23
(June 2009)
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GENERAL ITERATIVE ALGORITHMS FOR A COUNTABLE FAMILY OF NONEXPANSIVE MAPPINGS AND ITS APPLICATIONS
Kriengsak Wattanawitoon (Thailand), Poom Kumam (Thailand) and Usa Wannasingha Humphries (Thailand)
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Abstract:
In this paper, we propose two new general iterative algorithms for computing common fixed points of nonexpansive mappings in a Hilbert space and a Banach space, respectively. Under suitable conditions, we prove two strong convergence theorems for a countable family of nonexpansive mappings in Hilbert spaces and in uniformly smooth Banach spaces. These results improve and extend the results of Xu [14], and many others. |
| Keywords and phrases: strong convergence, nonexpansive mapping, countable family, equilibrium problem. |
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