Generalization of Ky Fan's Minimax Inequality

HAN Min

doi:10.3969/j.issn.0254-0037.2003.01.020

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Journal of Beijing University of Technology > 2003 > 29(1): 83-86. > DOI: 10.3969/j.issn.0254-0037.2003.01.020

HAN Min. Generalization of Ky Fan's Minimax Inequality[J]. Journal of Beijing University of Technology, 2003, 29(1): 83-86. DOI: 10.3969/j.issn.0254-0037.2003.01.020

Citation:

HAN Min. Generalization of Ky Fan's Minimax Inequality[J]. Journal of Beijing University of Technology, 2003, 29(1): 83-86. DOI: 10.3969/j.issn.0254-0037.2003.01.020

Citation:

HAN Min. Generalization of Ky Fan's Minimax Inequality[J]. Journal of Beijing University of Technology, 2003, 29(1): 83-86. DOI: 10.3969/j.issn.0254-0037.2003.01.020

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Generalization of Ky Fan's Minimax Inequality

HAN Min

College of Applied Sciences, Beijing University of Technology, Beijing 100022, China

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Received Date: July 16, 2002
Available Online: November 10, 2022

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Based on the property of convex and compactly closed set,the author generalizes Ky Fan minimax inequality as new minimax inequality of two functions on the product space of a topological vector space and a topological space,and from this obtains a minimax inequality about one function on this product space.At the same time a section theorem is also obtained,which is the generalization of many former section theorems.It has been verified that the obtained section theorem and minimax inequality are equivalent,the former being the geometrical form of the latter.
- topological space,
- Hausdorff topological vector space,
- minimax inequality,
- section theorem,
- convex space,
- semi-continuous,
- quasi-concave,
- compactly closed set

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[1]	FAN K. A minimax inequality and applications[A]. Inequalities Ⅲ[C]. New York:Academic Press, 1972. 103-113.
[2]	YEN C L. A minimax inequality and its applications to variational inequalities[J]. Pac J Math, 1981, 97(2):477-481.
[3]	程曹宗.与Tychonov不动点定理相关的几个结果[J].北京工业大学学报,1997,23(3):67-72.
[4]	PARK S. Generalizations of Ky Fan's matching theorems and their applications[J]. J Math Anal Appl, 1989,141:164-176.
[5]	张石生.变分不等式和相补问题——理论及应用[M].上海:上海科学技术文献出版社,1991.

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