Equilibrium existence theorems in KKM spaces |
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Authors: | Sehie Park |
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Institution: | The National Academy of Sciences, Republic of Korea; Department of Mathematical Sciences, Seoul National University, Seoul 151–747, Republic of Korea |
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Abstract: | An abstract convex space satisfying the KKM principle is called a KKM space. This class of spaces contains G-convex spaces properly. In this work, we show that a large number of results in KKM theory on G-convex spaces also hold on KKM spaces. Examples of such results are theorems of Sperner and Alexandroff–Pasynkoff, Fan–Browder type fixed point theorems, Horvath type fixed point theorems, Ky Fan type minimax inequalities, variational inequalities, von Neumann type minimax theorems, Nash type equilibrium theorems, and Himmelberg type fixed point theorems. |
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Keywords: | primary 47H04 47H10 secondary 46A16 46A55 52A07 54C60 54H25 91B50 |
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