Abstract and Applied Analysis

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

Somyot Plubtieng and Wanna Sriprad

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 301305, 18 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313170921

Digital Object Identifier
doi:10.1155/2010/301305

Mathematical Reviews number (MathSciNet)
MR2739685

Zentralblatt MATH identifier
1207.65074

Citation

Plubtieng, Somyot; Sriprad, Wanna. Iterative Schemes for Fixed Points of Relatively Nonexpansive Mappings and Their Applications. Abstr. Appl. Anal. 2010 (2010), Article ID 301305, 18 pages. doi:10.1155/2010/301305. https://projecteuclid.org/euclid.aaa/1313170921


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