Hybrid Extragradient-Type Methods for Finding a Common Solution of an Equilibrium Problem and a Family of Strict Pseudo-Contraction Mappings

Affiliation(s)

Posts and Telecommunications Institute of Technology, Hanoi, Vietnam.

Hanoi University of Science, Hanoi, Vietnam.

Graduate student, Hanoi Institute of Mathematics, Hanoi, Vietnam.

Posts and Telecommunications Institute of Technology, Hanoi, Vietnam.

Hanoi University of Science, Hanoi, Vietnam.

Graduate student, Hanoi Institute of Mathematics, Hanoi, Vietnam.

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.

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.

Cite this paper

P. Anh, T. Quoc and D. Son, "Hybrid Extragradient-Type Methods for Finding a Common Solution of an Equilibrium Problem and a Family of Strict Pseudo-Contraction Mappings,"*Applied Mathematics*, Vol. 3 No. 10, 2012, pp. 1357-1367. doi: 10.4236/am.2012.330192.

P. Anh, T. Quoc and D. Son, "Hybrid Extragradient-Type Methods for Finding a Common Solution of an Equilibrium Problem and a Family of Strict Pseudo-Contraction Mappings,"

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