Abstract
The purpose of this paper is to obtain a generalization of the famous Browder's fixed point theorem and some equivalent forms. As application, these results are utilized to study the existence problems of fixed points and nearest points.
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References
Browder F. The fixed point theory of multivalued mappings in topological vector space [J].Math Ann, 1968,177:183–301.
Zhang Shisheng.The Theory of Variational Inequalities and Complement-Arity Problems With Applications [M]. Shanghai: Shanghai Scientific and Technological Literature Publishing House, 1991. (in Chinese)
Tarafdar E. On nonlinear variational inequalities[J].Proc Amer Math Soc, 1977,67:95–98.
Tarafdar E. A fixed point theorem equivalent to Fan-Knaster-Kuratowski-Mazurkieweicz's theorem[J].J Math Anal Appl, 1987,128:475–479.
Tarafdar E. Five equivalent theorems on a convex subset of a topological vector spaces [J].Comment Math Univ Caroline, 1989,30(2):323–326.
Tian G Q. Generalizations of KKM theorem and the Ky Fan minimax inequality with applications to maximal elements, price equilibrium and complementarity[J].J Math Anal Appl, 1992,170:457–471.
Chang Shih-sen, Cho Y J, Wu X, Zhang Y. The topological versions of KKM theorem and Fan's matching theorem with applications[J].Topological Methods in Nonlinear Anal, 1993,1:231–245.
Kindler J. Topological intersection theorems[J].Proc Amer Math Soc, 1993,117:1003–1011.
Allen G. Variational inequalities, complementarity problems and duality theorem [J].J Math Anal Appl, 1977,58:1–10.
Fan Ky. A minimax inequality and applications [A]. In: Shisha O Ed.Inequalities III [C]. Academic Press, 1972.
Fan Ky. A generalization of Tychonoff's fixed point theorem[J].Math Ann, 1961,141:303–310.
Fan Ky. Some properties of convex sets related to fixed point theorems[J].Math Ann, 1984,266:519–537.
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Foundation item: the National Natural Science Foundation of China (19971058)
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Shisheng, Z., Xian, Z. A generalization of Browder's fixed point theorem with applications. Appl Math Mech 20, 943–951 (1999). https://doi.org/10.1007/BF02459056
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DOI: https://doi.org/10.1007/BF02459056
Key words
- transfer open (closed) mapping
- Browder's fixed point theorem
- transfer upper (lower) semi-continuoun function