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2008•Journal of Chongqing Technology and Business UniversityRequires access

The iterations for variational inequalities and nonexpansive mapping

Dao-Jun Wen

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Abstract

In this paper,a class of variational inequalities and Wiener-Hopf equations are introduced, which involve nonexpansive operators.The alternative equivalent formulations is deduced by using the projection technique.A iterative method is proposed for finding the common element of the set of the nonexpansive map- pings' fixed points and the variational inequalities' solution.The convergence criteria of the iterative method is proved under some mild conditions.The results in this paper may be viewed as an improvement and refinement of the previously known results for variational inequalities.

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What this paper is about

In this paper,a class of variational inequalities and Wiener-Hopf equations are introduced, which involve nonexpansive operators.The alternative equivalent formulations is deduced by using the projection technique.A iterative method is proposed for finding the common element of the set of the nonexpansive map- pings' fixed points and the variational inequalities' solution.The convergence criteria of the iterative method is proved under some mild conditions.The results in this paper may be viewed as an improvement and refinement of the previously known results for variational inequalities.

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Available abstract

In this paper,a class of variational inequalities and Wiener-Hopf equations are introduced, which involve nonexpansive operators.The alternative equivalent formulations is deduced by using the projection technique.A iterative method is proposed for finding the common element of the set of the nonexpansive map- pings' fixed points and the variational inequalities' solution.The convergence criteria of the iterative method is proved under some mild conditions.The results in this paper may be viewed as an improvement and refinement of the previously known results for variational inequalities.

Key concepts: Variational inequality, Mathematics, Convergence (economics), Projection (relational algebra), Iterative method, Applied mathematics, Fixed point, Set (abstract data type)

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