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Hybrid Extragradient-Type Methods for Finding a Common Solution of an Equilibrium Problem and a Family of Strict Pseudo-Contraction Mappings
Posts and Telecommunications Institute of Technology, Hanoi, Vietnam
Hanoi University of Science, Hanoi, Vietnam
Graduate student, Hanoi Institute of Mathematics, Hanoi, Vietnam
- 1 Posts and Telecommunications Institute of Technology, Hanoi, Vietnam
- 2 Hanoi University of Science, Hanoi, Vietnam
- 3 Graduate student, Hanoi Institute of Mathematics, Hanoi, Vietnam
Applied Mathematics·Volume 03 (2012)·Pages 1357–1367·Published 31 October 2012·DOI10.4236/am.2012.330192
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Abstract
This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.
KeywordsEquilibrium ProblemsFixed PointPseudo-MonotoneLipschitz-Type ContinuityExtragradient MethodStrict Pseudo-Contraction Mapping
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