摘 要
在本論文中，我們得到一個在L-凸空間上的交集定理，此定理推廣了文獻[27]中的主要定理。利用這個定理，我們證得了一些固定點定理、最大元素定理、同值點定理和大中取小不等式存在性定理。本文的結果推廣了許多學者的研究結果。

In this paper, we obtain a new intersection theorem in L-convex spaces, this theorem generalizes and improves the main result of Lu and Tang [27]. As applications, we get a fixed point theorem, a maximal element theorem, a coincidence theorem, and some existence theorems concerning minimax inequalities in L-convex spaces. Our results generalize many well-known results.

REFERENCES
[1] Q. H. Ansari, A. Idzik, and J. C. Yao, Coincidence and fixed point theorems with applications, Topol. Methods Nonlinear Anal. 15(2000), 191-202.
[2] F.E. Browder, Coincidence theorems, minimax theorems, and variational inequalities, Contemp. Math. 26(1984) 47–80.
[3] H. Ben-El-Mechaiekh, P. Deguire, and A. Granas, Points fixes et coincidences pour les functions multivoques II, C. R. Acad. Sci. Paris Ser. I 295(1982), 381-388.
[4] K. L. Cheng, Coincidence Theorems, Generalized G-s-KKM Theorems and Their Applications, graduate Institute of Mathematics and Science, NHCTC, Hsin Chu, Taiwan.(2006).
[5] S. S. Chang and Y. Zhang, Generalized KKM theorem and variational inequalities, J. Math. Anal. Appl. 159(1991), 208-233.
[6] S. S. Chang, B. S. Lee, X. Wu, Y. J. Cho, and G. M. Lee, On the generalized quasivariational inequality problems, J. Math. Anal. Appl. 203(1996), 686-711.
[7] P. Deguire and M. Lassonde, Familles selectantes, Topol. Methods Nonlinear Anal. 5(1995), 261-269.
[8] P. Deguire, K. K. Tan, and G. X. Z. Yuan, The study of maximal elements, fixed point for -majorized mappings and their applications to minimax and variational inequalities in product topological spaces, Nonlinear Anal. 37(1999), 933-951.
[9] X. P. Ding, Best approximation and coincidence theorems, J. Sichuan Normal Univ. Nat. Sci. 18(1995), 21-29.
[10] X. P. Ding, Coincidence theorems in topological spaces and their applications, applied. Math. Lett. 12(1999), 99-105.
[11] X. P. Ding, Existence of solutions for quasi-equilibrium problems in noncompact topological spaces, Comput. Math. Appl. 39(2000), 13-21.
[12] X.P. Ding, Generalized L-KKM Type Theorems in L-Convex with Applications, Computers Math. Applic. 43(2002), 1249-1256.
[13] X.P. Ding, Generalized G-KKM theorems in generalized convex spaces and their applications, J. Math. Anal.Appl. 266 (2002) 21–37.
[14] K. Fan, A generalization of Tychonoff’s fixed point theorem, Math. Ann. 142(1961),305-310.
[15] K. Fan, A minimax inequality and applications, in: Inequalities, vol. 3, Academic Press, New York, 1972, pp. 103–113.
[16] K. Fan, Some properties of convex sets relation to fixed point theorems, Math. Ann. 266 (1984) 519–537.
[17] A. Granas and F. C. Liu, Coincidence for set valued maps and inequalities, J. Math. Anal. Appl. 165(1986), 119-148.
[18] C.W. Ha, Minimax and fixed point theorems, Math. Ann. 248 (1980) 73–77.
[19] C.W. Ha, On a minimax inequality of Ky Fan, Proc. Amer. Math. Soc. 99 (1987) 680–682.
[20] B. Knaster, C. Kuratowski, and S. Mazurkiewicz, Ein Beweis des Fixpunksatzes fur n-dimensionale simplexe, Fund. Math. 14(1929),132-137.
[21] H. Kormiya, Coincidence theorems and saddle point, Proc. Amer. Math. Soc. 96 (1986) 59–62.
[22] F. J. Liu, On a form of KKM principle and supinfsup inequalities of von Neumann and Ky Fan type, J. Math. Anal. Appl. 155(1991), 420-436.
[23] L. J. Lin, Q. H. Ansari, and J. Y. Wu, Geometric properties and coincidence theorems with applications to generalized vector equilibrium problems, J. Optim. Theory Appl. 117(1)(2003), 121-137.
[24] L. J. Lin and H. I. Chen, Coincidence theorems for family of multimaps and their applications to equilibrium problems, J. Abstr. Anal. 5(2003), 295-305.
[25] L.J. Lin, Z.T. Yu, Q.H. Ansari, L.P. Lai, Fixed point and maximal theorems with applications to abstract economies and minimax inequalities, J. Math. Anal. Appl. 284 (2003) 656–671.
[26] M. Lassonde, On the use of KKM multifunctions in fixed point theory and related topics, J. Math. Anal. Appl. 97(1983), 151-201.
[27] H. Lu, D. Tang, An intersection theorem in L-convex spaces with applications, J. Math. Anal. Appl. 312 (2005) 343–356
[28] Y. J. Lin and G. Tina, Minimax inequalities equivalent to the Fan-Knaster- Kuratowski-Mazurkiewicz theorem, Appl. Math. Optim. 28(1993), 173-179.
[29] J. von Neumann, Uber ein okonomsiches Gleichungssystem und eine Verallgemeinering des Browerschen Fixpunktsatzes, Ergeb. Math. Kolloq. 8(1937), 73-83.
[30] S. Park, Foundations of the KKM theory via coincidences of composites of upper semi-continuous maps, J. Korean Math. Soc. 31(1994), 164-176.
[31] N. Shioji, A further generalization of the Knaster-Kuratowski-Mazurkiewicz theorem, Proc. Amer. Math. Soc. 111(1991), 187-195.
[32] E. Tarafdar, On nonlinear variational inequalities, Proc. Amer. Math. Soc. 67(1977)95-98
[33] G. Q. Tina, Generalized KKM theorem, minimax inequalities and their applications, J. Optim. Theory Appl. 83(1994), 375-389.
[34] G. Tina and J. Zhou, Transfer continuities, generalizations of the Weierstrass and maximum theorems: a full characterization, J. Math. Econom. 24(1995), 281-303.
[35] X. Wu, F. Li, On Ky Fan’s section theorem, J. Math. Anal. Appl. 227 (1998) 112–121.
[36] J.H. Zhang, R.Y. Ma, Minimax inequalities of Ky Fan, Appl. Math. Lett. 11 (1998) 37–41.
[37] Z. T. Yu and L. J. Lin, Continuous selection and fixed point theorems, Nonlinear Anal. 52(2003), 445-453.