Title:
|
Admissible maps, intersection results, coincidence theorems (English) |
Author:
|
Balaj, Mircea |
Language:
|
English |
Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
ISSN:
|
0010-2628 (print) |
ISSN:
|
1213-7243 (online) |
Volume:
|
42 |
Issue:
|
4 |
Year:
|
2001 |
Pages:
|
753-762 |
. |
Category:
|
math |
. |
Summary:
|
We obtain generalizations of the Fan's matching theorem for an open (or closed) covering related to an admissible map. Each of these is restated as a KKM theorem. Finally, applications concerning coincidence theorems and section results are given. (English) |
Keyword:
|
acyclic map |
Keyword:
|
convex space |
Keyword:
|
matching theorem |
Keyword:
|
coincidence theorem |
MSC:
|
47H10 |
MSC:
|
54C60 |
MSC:
|
54H25 |
idZBL:
|
Zbl 1068.47068 |
idMR:
|
MR1883383 |
. |
Date available:
|
2009-01-08T19:18:26Z |
Last updated:
|
2012-04-30 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119290 |
. |
Reference:
|
[1] Allen G.: Variational inequalities, complementary problems and duality theorems.J. Math. Anal. Appl. 58 (1977), 1-10. MR 0513305 |
Reference:
|
[2] Balaj M.: A variant of a fixed point theorem of Browder and some applications.Math. Montisnigri 9 (1998), 5-13. Zbl 0999.47045, MR 1657668 |
Reference:
|
[3] Ben-El-Mechaiekh H., Deguire P., Granas A.: Points fixes et coincidences pour les applications multivoque, $I$.C.R. Acad. Sci. Paris 295 (1982), 337-340; II, 381-384. |
Reference:
|
[4] Browder F.E.: The fixed point theory of multi-valued mappings in topological vector spaces.Math. Ann. 177 (1968), 283-301. Zbl 0176.45204, MR 0229101 |
Reference:
|
[5] Chang S.Y.: A generalization of KKM principle and its applications.Soochow J. Math. 15 (1989), 7-17. Zbl 0747.47033, MR 1025967 |
Reference:
|
[6] Ding X.-P., Tan K.-K.: Matching theorems, fixed point theorems, and minimax inequalities without convexity.J. Austral. Math. Soc. (Ser. A) 49 (1990), 111-128. Zbl 0709.47053, MR 1054086 |
Reference:
|
[7] Fan K.: A generalization of Tychonoff's fixed point theorem.Math. Ann 142 (1961), 305-310. Zbl 0093.36701, MR 0131268 |
Reference:
|
[8] Fan K.: A minimax inequality and applications.in ``Inequalities III'', O Shisha (ed.), Academic Press, New York, 1972, pp.103-113. Zbl 0302.49019, MR 0341029 |
Reference:
|
[9] Fan K.: Fixed-point and related theorems for non-compact convex sets.in ``Game Theory and Related Topics'', O. Moeschlin and D. Pallaschke (eds.), North-Holland, Amsterdam, 1979, pp.151-156. Zbl 0432.54040, MR 0556363 |
Reference:
|
[10] Fan K.: Some properties of convex sets related to fixed point theorems.Math. Ann. 266 (1984), 519-537. Zbl 0515.47029, MR 0735533 |
Reference:
|
[11] Gorniewicz L.: A Lefschetz-type fixed point theorem.Fund. Math. 88 (1975), 103-115. Zbl 0306.55007, MR 0391062 |
Reference:
|
[12] Gorniewicz L.: Homological methods in fixed point theory of multi-valued maps.Dissertationes Math. 129 (1976), 1-71. Zbl 0324.55002, MR 0394637 |
Reference:
|
[13] Ha C.-W.: Minimax and fixed point theorems.Math. Ann. 248 (1980), 73-77. Zbl 0413.47042, MR 0569411 |
Reference:
|
[14] Kim W.K.: Some applications of the Kakutani fixed point theorem.J. Math. Anal. Appl. 121 (1987), 119-122. Zbl 0612.54055, MR 0869523 |
Reference:
|
[15] Lassonde M.: On the use of KKM multifunctions in fixed point theory and related topics.J. Math. Anal. Appl. 97 (1983), 151-201. Zbl 0527.47037, MR 0721236 |
Reference:
|
[16] Lassonde M.: Sur le principle KKM.C.R. Acad. Sci. Paris 310 (1990), 573-576. MR 1050134 |
Reference:
|
[17] Lin T.-C.: Convex sets, fixed points, variational and minimax inequalities.Bull. Austral. Math. Soc. (Ser. A) 34 (1986), 107-117. Zbl 0597.47038, MR 0847978 |
Reference:
|
[18] Park S.: Generalizations of Ky Fan's matching theorems and their applications.J. Math. Anal. Appl. 141 (1989), 164-176. Zbl 0681.47028, MR 1004591 |
Reference:
|
[19] Park S.: Convex spaces and KKM families of subsets.Bull. Korean Math. Soc. 27 (1990), 11-14. Zbl 0746.47036, MR 1060811 |
Reference:
|
[20] Park S.: Generalizations of Ky Fan's matching theorems and their applications, $II$.J. Korean Math. Soc. 28 (1991), 275-283. Zbl 0813.47063, MR 1127832 |
Reference:
|
[21] Park S.: Some coincidence theorems on acyclic multifunctions and applications to KKM theory.in ``Fixed Point Theory and Applications'' (K.-K. Tan ed.), World Scientific, Publishing River Edge, NY, 1992, pp.248-277. MR 1190044 |
Reference:
|
[22] Park S.: Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps.J. Korean Math. Soc. 31 (1994), 493-519. Zbl 0829.49002, MR 1297433 |
Reference:
|
[23] Park S.: Ninety years of the Browder fixed point theorem.Vietnam J. Math. 27 (1999), 193-232. MR 1811334 |
Reference:
|
[24] Park S., Kim H.: Coincidences of composites of u.s.c. maps on $H$-spaces and applications.J. Korean Math. Soc. 32 (1995), 251-264. Zbl 0868.54015, MR 1338994 |
Reference:
|
[25] Sehgal V.M., Singh S.P., Whitfield J.H.M.: KKM-maps and fixed point theorems.Indian J. Math. 32 (1990), 289-296. MR 1088610 |
Reference:
|
[26] Shih M.-H.: Covering properties of convex sets.Bull. London Math. Soc. 18 ((1986)), 57-59. Zbl 0579.52004, MR 0841369 |
Reference:
|
[27] Shih M.-H., Tan K.-K.: Covering theorems of convex sets related to fixed-point theorems.in ``Nonlinear and Convex Analysis-Proc. in Honor of Ky Fan'' (B-L. Lin and S. Simons, eds.), Marcel Dekker, New York, 1987, pp.235-244. Zbl 0637.47029, MR 0892795 |
Reference:
|
[28] Shih M.-H., Tan K.K.: A geometric property of convex sets with applications to minimax type inequalities and fixed point theorems.J. Austral. Math. Soc. 45 (1988), 169-183. Zbl 0664.52001, MR 0951575 |
Reference:
|
[29] Shioji N.: A further generalization of the Knaster-Kuratowski-Mazurkiewicz theorems.Proc. Amer. Math. Soc. 111 (1991), 187-195. MR 1045601 |
Reference:
|
[30] Takahashi W.: Nonlinear variational inequalities and fixed point theorems.J. Math. Soc. Japan 28 (1976), 168-181. Zbl 0314.47032, MR 0399979 |
Reference:
|
[31] Tarafdar E.: On nonlinear variational inequalities.Proc. Amer. Math. Soc. 67 (1977), 95-98. Zbl 0369.47029, MR 0467408 |
Reference:
|
[32] Tarafdar E.: On minimax principles and sets with convex sections.Publ. Math. Debrecen 29 (1982), 219-226. Zbl 0536.47038, MR 0678897 |
. |