Generalized convexity and generalized quasi-variational inequality (Q2732232)
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scientific article; zbMATH DE number 1623408
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalized convexity and generalized quasi-variational inequality |
scientific article; zbMATH DE number 1623408 |
Statements
27 February 2002
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\(G\)-convex spaces
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\(G\)-convex sets
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generalized quasi-variational inequalities
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Generalized convexity and generalized quasi-variational inequality (English)
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The generalized convex space (or \(G\)-convex space) is studied in [\textit{S. Park} and \textit{H. Kim}, J. Math. Anal. Appl. 197, No. 1, 173-187 (1996; Zbl 0851.54039)]. In this paper, the author further studies some properties of \(G\)-convex spaces and \(G\)-convex sets. As usual, the existence of a solution of generalized quasi-variational inequalities is given by using the continuous selection theorem and a Browder type fixed point theorem in the setting of \(G\)-convex spaces studied in [\textit{X. Zhang}, J. Nanjing Univ., Math. Biq. 14, No. 2, 232-237 (1997; Zbl 0899.47042)].
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0.8383651971817017
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0.8352811336517334
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