, Volume 128, Issue 1, pp 191-201

Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings

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Abstract

In this paper, we introduce an iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The iterative process is based on the so-called extragradient method. We obtain a weak convergence theorem for two sequences generated by this process

Communicated by S. Schaible