Taiwanese Journal of Mathematics

CONVERGENCE ANALYSIS OF A HYBRID RELAXED-EXTRAGRADIENT METHOD FOR MONOTONE VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS

Lu-Chuan Ceng, B. T. Kien, and N. C. Wong

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Abstract

In this paper we introduce a hybrid relaxed-extragradient method for finding a common element of the set of common fixed points of $N$ nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The hybrid relaxed-extragradient method is based on two well-known methods: hybrid and extragradient. We derive a strong convergence theorem for three sequences generated by this method. Based on this theorem, we also construct an iterative process for finding a common fixed point of $N+1$ mappings, such that one of these mappings is taken from the more general class of Lipschitz pseudocontractive mappings and the rest $N$ mappings are nonexpansive.

Article information

Source
Taiwanese J. Math., Volume 12, Number 9 (2008), 2549-2568.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405195

Digital Object Identifier
doi:10.11650/twjm/1500405195

Mathematical Reviews number (MathSciNet)
MR2479071

Zentralblatt MATH identifier
1220.47085

Subjects
Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40]

Keywords
variational inequality nonexpansive mapping extragradient method hybrid method monotone mapping fixed point strong convergence demiclosedness principle Opial's condition

Citation

Ceng, Lu-Chuan; Kien, B. T.; Wong, N. C. CONVERGENCE ANALYSIS OF A HYBRID RELAXED-EXTRAGRADIENT METHOD FOR MONOTONE VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS. Taiwanese J. Math. 12 (2008), no. 9, 2549--2568. doi:10.11650/twjm/1500405195. https://projecteuclid.org/euclid.twjm/1500405195


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