An implicit iterative scheme for monotone variational inequalities and fixed point problems |
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Authors: | LC Ceng P Cubiotti JC Yao |
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Institution: | 1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;2. Department of Mathematics, University of Messina, Contrada Papardo, Salita Sperone 31, 98166 Messina, Italy;3. Department of Applied Mathematics, National Sun Yat-sen University, 804 Kaohsiung, Taiwan |
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Abstract: | In this paper we introduce an implicit iterative scheme 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 implicit iterative scheme is based on two well-known methods: extragradient and approximate proximal. We obtain a weak convergence theorem for three sequences generated by this implicit iterative scheme. On the basis of this theorem, we also construct an implicit 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 other N mappings are nonexpansive. |
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Keywords: | 47H09 47J20 |
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