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

Somyot Plubtieng and Wanna Sriprad

Abstract and Applied Analysis, 2010, vol. 2010, issue 1

Abstract: 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.

Date: 2010
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https://doi.org/10.1155/2010/301305

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:301305

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