An Extragradient Approximation Method for Equilibrium Problems and Fixed Point Problems of a Countable Family of Nonexpansive Mappings

By Rabian Wangkeeree. 2008

56 citations recorded by the source corpus.

We introduce a new iterative scheme for finding the common element of the set of common fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the variational inequality. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. Moreover, we apply our result to the problem of finding a common fixed point of a countable family of nonexpansive mappings, and the problem of finding a zero of a monotone operator. This main theorem extends a recent result of Yao et al. (2007) and many others.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c6b4d10ebc43a84cf3d21903bbef457fcbf2434e

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In Computational Theory and Mathematics

1. Kriengsak Wattanawitoon
2. Narin Petrot
3. Poom Kumam
4. Jong Kyu Kim

In Geometry and Topology

1. Poom Kumam
2. Kriengsak Wattanawitoon
3. Narin Petrot
4. Jong Kyu Kim
5. Wutiphol Sintunavarat

In Numerical Analysis

1. Narin Petrot
2. Kriengsak Wattanawitoon
3. Poom Kumam
4. Jong Kyu Kim

Citations in the corpus

• A hybrid projection method for generalized mixed equilibrium problems and fixed point problems in Banach spaces (2010, background): “Recently, many authors studied the problem of finding a common element of the set of fixed points of nonexpansive or relatively nonexpansivemappings and the set of solutions of (generalized ormixed) equilibrium problems in the framework ofHilbert spaces andBanach spaces respectively; see, for instan”