COMMENTS ON HOU JICHENG’S “ON SOME KKM TYPE THEOREMS”
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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.
Abstract
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.
참고문헌 (7)
- X.-P. Ding, "New H-KKM theorems and their applications to geometric property, coincidence theorems, minimax inequality and maximal elements", Indian J. Pure Appl. Math., 26(1), pp.1~19 (1995)
- J. Hou, "On some KKM type theorems", Adv. Math., 36(1), pp.86~88 (2007)
- E. M. Kalmoun, "Topological KKM theorems and generalized vector equilibria on G-convex spaces with applications", Proc. Amer. Math. Soc., 129(5), pp.1335~1348 (2001)
- 박세희, "COMMENTS ON GENERALIZED R-KKM TYPE THEOREMS", 대한수학회논문집, 25(2), pp.303~311 (2010), 대한수학회
- S. Park, "Fixed point theorems in the new era of the KKM theory, Fixed Point Theory and Its Applications (Proc. ICFPTA-2009)" (2009), Yokohama Publ.
- S. Park, "General KKM theorems for abstract convex spaces", J. Inform. Math. Sci., 1(1), pp.1~13 (2009)
- S. Park, "Generalizations of the KKM type theorems on generalized convex spaces", Indian J. Pure Appl. Math., 29(2), pp.121~132 (1998)