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In a paper by Hou Jicheng, On some KKM type theorems,Advaces in Mathematics 36 (2007), no. 1, 86–88, the author claimed that some previous KKM type theorems are false by giving a counterexample.
In the present paper, we show that the counterexample does not work and, consequently, the results are correct. Moreover, we claim that the artificial concept like transfer compactly closed-valued maps can be destroyed.
Finally, we introduce a theorem generalizing the main target of Hou.
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참고문헌 (7)
참고문헌 신청
E. M. Kalmoun / 2001 / Topological KKM theorems and generalized vector equilibria on G-convex spaces with applications / Proc. Amer. Math. Soc. 129 (5) : 1335 ~ 1348
J. Hou / 2007 / On some KKM type theorems / Adv. Math. 36 (1) : 86 ~ 88
S. Park / 1998 / Generalizations of the KKM type theorems on generalized convex spaces / Indian J. Pure Appl. Math. 29 (2) : 121 ~ 132
S. Park / 2009 / Fixed point theorems in the new era of the KKM theory, Fixed Point Theory and Its Applications (Proc. ICFPTA-2009) / Yokohama Publ.
S. Park / 2009 / General KKM theorems for abstract convex spaces / J. Inform. Math. Sci. 1 (1) : 1 ~ 13
J. Hou / 2007 / On some KKM type theorems / Adv. Math. 36 (1) : 86 ~ 88
S. Park / 1998 / Generalizations of the KKM type theorems on generalized convex spaces / Indian J. Pure Appl. Math. 29 (2) : 121 ~ 132
S. Park / 2009 / Fixed point theorems in the new era of the KKM theory, Fixed Point Theory and Its Applications (Proc. ICFPTA-2009) / Yokohama Publ.
S. Park / 2009 / General KKM theorems for abstract convex spaces / J. Inform. Math. Sci. 1 (1) : 1 ~ 13
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