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Peng, Jian-Wen; Wu, Soon-Yi; Yao, Jen-Chih

A new iterative method for finding common solutions of a system of equilibrium problems, fixed-point problems, and variational inequalities. (English) Zbl 1206.47080

Abstr. Appl. Anal. 2010, Article ID 428293, 27 p. (2010).
Summary: We introduce a new iterative scheme based on extragradient method and viscosity approximation method for finding a common element of the solutions set of a system of equilibrium problems, fixed point sets of an infinite family of nonexpansive mappings, and the solution set of a variational inequality for a relaxed cocoercive mapping in a Hilbert space. We prove a strong convergence theorem. The results in this paper unify and generalize some well-known results in the literature.

Cited in 10 Documents

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

extragradient method; viscosity approximation method; nonexpansive mappings; relaxed cocoercive mapping; Hilbert space; strong a convergence
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\textit{J.-W. Peng} et al., Abstr. Appl. Anal. 2010, Article ID 428293, 27 p. (2010; Zbl 1206.47080)
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