Generic uniqueness of equilibrium points |
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Authors: | Jian YuDingtao Peng Shuwen Xiang |
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Institution: | a School of Science, Guizhou University, Guiyang 550025, Guizhou, Chinab School of Science, Beijing Jiaotong University, Beijing 100044, Chinac Academic Affairs Office, Guizhou University, Guiyang 550025, Guizhou, China |
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Abstract: | Let X be a nonempty, convex and compact subset of normed linear space E (respectively, let X be a nonempty, bounded, closed and convex subset of Banach space E and A be a nonempty, convex and compact subset of X) and f:X×X→R be a given function, the uniqueness of equilibrium point for equilibrium problem which is to find x∗∈X (respectively, x∗∈A) such that f(x∗,y)≥0 for all y∈X (respectively, f(x∗,y)≥0 for all y∈A) is studied with varying f (respectively, with both varying f and varying A). The results show that most of equilibrium problems (in the sense of Baire category) have unique equilibrium point. |
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Keywords: | 47H14 54C60 |
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