Weakly <em>R</em>-KKM Mappings—Intersection Theorems and Minimax Inequalities in Topological Spaces

DENG Lei; YANG Ming-ge

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DENG Lei, YANG Ming-ge. Weakly R-KKM Mappings—Intersection Theorems and Minimax Inequalities in Topological Spaces[J]. Applied Mathematics and Mechanics, 2007, 28(1): 92-98.

Citation:

DENG Lei, YANG Ming-ge. Weakly R-KKM Mappings—Intersection Theorems and Minimax Inequalities in Topological Spaces[J]. Applied Mathematics and Mechanics, 2007, 28(1): 92-98.

Citation:

DENG Lei, YANG Ming-ge. Weakly R-KKM Mappings—Intersection Theorems and Minimax Inequalities in Topological Spaces[J]. Applied Mathematics and Mechanics, 2007, 28(1): 92-98.

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Weakly R-KKM Mappings—Intersection Theorems and Minimax Inequalities in Topological Spaces

DENG Lei¹,
YANG Ming-ge^1,2

1.
School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China;

Received Date: 2005-10-09
Rev Recd Date: 2006-10-31
Publish Date: 2007-01-15

Abstract

Abstract

The concepts of weakly R-KKM mappings, R-convex and R-β-quasiconvex in general topological spaces without any convex structure are introduced. Relating to these, an extension to general topological spaces of Fan's matching theorem is obtained, namely Lemma 1.2. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. The results generalize and improve the corresponding results in the literature.
- weakly R-KKM mapping,
- R-convex,
- R-β-quasiconvex,
- generalized R-KKM mapping

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References(12)

References

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