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.
Citation
Lu-Chuan Ceng. B. T. Kien. N. C. Wong. "CONVERGENCE ANALYSIS OF A HYBRID RELAXED-EXTRAGRADIENT METHOD FOR MONOTONE VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS." Taiwanese J. Math. 12 (9) 2549 - 2568, 2008. https://doi.org/10.11650/twjm/1500405195
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