Iterative Methods for Pseudomonotone Variational Inequalities and Fixed-Point Problems |
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Authors: | Yonghong Yao Mihai Postolache |
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Institution: | 1. Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China 2. Faculty of Applied Sciences, University ??Politehnica?? of Bucharest, Splaiul Independentei 313, Bucharest, 060042, Romania
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Abstract: | In this paper, we introduce an iterative scheme for finding a common element of the set of solution of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known schemes: extragradient and approximate proximal methods. We derive some necessary and sufficient conditions for strong convergence of the sequences generated by the proposed scheme. |
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