Weak Convergence of an Iterative Method for Pseudomonotone Variational Inequalities and Fixed-Point Problems
We consider an iterative scheme for finding a common element of the set of solutions of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of N nonexpansive mappings. The proposed iterative method combines two well-known schemes: extragradient and approximate proximal methods. We derive a necessary and sufficient condition for weak convergence of the sequences generated by the proposed scheme.
KeywordsVariational inequalities Nonexpansive mappings Extragradient methods Approximate proximal methods Pseudomonotone mappings Fixed points Weak convergence Opial condition
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