TITLE:
Hybrid Extragradient-Type Methods for Finding a Common Solution of an Equilibrium Problem and a Family of Strict Pseudo-Contraction Mappings
AUTHORS:
Pham Ngoc Anh, Tran Dinh Quoc, Dang Xuan Son
KEYWORDS:
Equilibrium Problems; Fixed Point; Pseudo-Monotone; Lipschitz-Type Continuity; Extragradient Method; Strict Pseudo-Contraction Mapping
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.10A,
November
1,
2012
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.