Iterative Schemes for Fixed Points of Relatively Nonexpansive Mappings and Their Applications

We present two iterative schemes with errors which are proved to be strongly convergent to a common element of the set of fixed points of a countable family of relatively nonexpansive mappings and the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniforml...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2010-01, Vol.2010 (2010), p.705-722
Main Authors: Plubtieng, Somyot, Sriprad, Wanna
Format: Article
Language:English
Subjects:
Banach spaces
Hilbert space
Studies
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Summary:We present two iterative schemes with errors which are proved to be strongly convergent to a common element of the set of fixed points of a countable family of relatively nonexpansive mappings and the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniformly smooth and uniformly convex Banach space. Using the result we consider strong convergence theorems for variational inequalities and equilibrium problems in a real Hilbert space and strong convergence theorems for maximal monotone operators in a real uniformly smooth and uniformly convex Banach space.
ISSN:1085-3375
1687-0409
DOI:10.1155/2010/301305