\(F\)-implicit complementarity problems in Banach spaces (Q1884381)
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scientific article; zbMATH DE number 2112821
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(F\)-implicit complementarity problems in Banach spaces |
scientific article; zbMATH DE number 2112821 |
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\(F\)-implicit complementarity problems in Banach spaces (English)
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1 November 2004
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Summary: The \(F\)-implicit complementarity problem (F-ICP) and \(F\)-implicit variational inequality problem (F-IVIP) are introduced and studied. The equivalence between (F-ICP) and (F-IVIP) is presented under certain assumptions. Furthermore, we derive some new existence theorems of solutions for (F-ICP) and (F-IVIP) by using the Fan-Knaster-Kuratowski-Mazurkiewicz theorem [\textit{K. Fan}, Math. Ann. 142, 305--310 (1961; Zbl 0093.36701)] and \textit{T. C. Lin}'s theorem [Bull. Aust. Math. Soc. 34, 107--117 (1986; Zbl 0597.47038)] under some suitable assumptions without the monotonicity.
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\(F\)-implicit complementarity problem
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\(F\)-implicit variational inequality
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equivalence
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Knaster-Kuratowski-Mazurkiewicz-mapping
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