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.

An implicit iterative scheme for monotone variational inequalities and fixed point problems

CUBIOTTI, Paolo;
2008-01-01

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.
2008
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/1848043
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