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

Pham Ngoc Anh, Tran Dinh Quoc, Dang Xuan Son

Graduate student, Hanoi Institute of Mathematics, Hanoi, Vietnam.
Hanoi University of Science, Hanoi, Vietnam.
Posts and Telecommunications Institute of Technology, Hanoi, Vietnam.

DOI: 10.4236/am.2012.330192                

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.

Keywords

Equilibrium Problems; Fixed Point; Pseudo-Monotone; Lipschitz-Type Continuity; Extragradient Method; Strict Pseudo-Contraction Mapping

Conflicts of Interest

The authors declare no conflicts of interest.

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