Abstract
The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-KKM mappings with finitely metrically compactly closed values and finitely metrically compactly open values were established in H-metric spaces. These theorems generalized recent results of Khamsi and Yuan. As applications, some Ky Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers, fixed point theorems and minimax inequality are obtained in H-metric spaces. These results generalize a number of know results in recent literature.
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Paper from DING Xie-ping, Member of Editoral Committee, AMM
Foundation item: the National Natural Science Foundation of China (19871059)
Biography: DING Xie-ping (1938-), Professor
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Xie-ping, D., Fu-quan, X. GeneralizedH-KKM type theorems inH-metric spaces with applications. Appl Math Mech 22, 1140–1148 (2001). https://doi.org/10.1007/BF02436450
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DOI: https://doi.org/10.1007/BF02436450
Key words
- hyperconvex space
- H-metric space
- finitely metrically compactly closed (open) set
- generalizedH-KKM mapping
- admissible set