Title:
|
Generalizations of the Fan-Browder fixed point theorem and minimax inequalities (English) |
Author:
|
Balaj, Mircea |
Author:
|
Muresan, Sorin |
Language:
|
English |
Journal:
|
Archivum Mathematicum |
ISSN:
|
0044-8753 (print) |
ISSN:
|
1212-5059 (online) |
Volume:
|
41 |
Issue:
|
4 |
Year:
|
2005 |
Pages:
|
399-407 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
In this paper fixed point theorems for maps with nonempty convex values and having the local intersection property are given. As applications several minimax inequalities are obtained. (English) |
Keyword:
|
map |
Keyword:
|
fixed point |
Keyword:
|
local intersection property |
Keyword:
|
minimax inequality |
MSC:
|
47H10 |
MSC:
|
49J35 |
MSC:
|
54C60 |
MSC:
|
54H25 |
idZBL:
|
Zbl 1111.54032 |
idMR:
|
MR2195493 |
. |
Date available:
|
2008-06-06T22:46:42Z |
Last updated:
|
2012-05-10 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107969 |
. |
Reference:
|
[1] 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:
|
[2] Balaj M.: Applications of two matching theorems in generalized convex spaces.Nonlinear Anal. Forum 7 (2002), 123–130. Zbl 1034.54016, MR 1959938 |
Reference:
|
[3] Ben-El-Mechaiekh H., Deguire P., Granas A.: Point fixes et coincidences pour les applications multivoques.C. R. Acad. Sci. Paris 295 (1982), I 337–340, II 381–384. |
Reference:
|
[4] Browder F. E.: The fixed point theory of multivalued mappings in topological vector spaces.Math. Ann. 177 (1968), 238–301. MR 0229101 |
Reference:
|
[5] Browder F. E.: Coincidence theorems, minimax theorems and variational inequalities.Conference in Modern Analysis and Probability, New Heaven, Conn., 1982: Contemp. Math. 26, pp. 67–80 (Amer. Math. Soc. Providence, RI., 1984). MR 0737389 |
Reference:
|
[6] Deguire P.: Browder-Fan fixed point theorem and related results.Discuss. Math. Differential Incl. 15 (1995), 149–162. Zbl 0931.47041, MR 1390397 |
Reference:
|
[7] Deguire P., Lassonde M.: Families sélectantes.Topol. Methods Nonlinear Anal. 5 (1995), 261–269. MR 1374063 |
Reference:
|
[8] Ding X. P.: New H-KKM theorems and equilibria of generalized games.Indian J. Pure Appl. Math. 27 (1996), 1057–1071. MR 1420096 |
Reference:
|
[9] Ding X. P.: A coincidence theorem involving contractible spaces.Appl. Math. Lett. 10 (1997), 53–56. Zbl 0879.54055, MR 1457639 |
Reference:
|
[10] Fan K.: A generalization of Tichonoff’s fixed point theorems.Math. Ann. 142 (1961), 305–310. MR 0131268 |
Reference:
|
[11] Fan K.: Sur une théorème minimax.C.R. Acad. Sci. Paris 259 (1964), 3925–3928. MR 0174955 |
Reference:
|
[12] Fan K.: A minimax inequality and applications.In: Inequalities III (O. Shisha, ed.), pp. 103–113, Academic Press, New York, 1972. Zbl 0302.49019, MR 0341029 |
Reference:
|
[13] Himmelberg C. J.: Fixed points of compact multifunctions.J. Math. Anal. Appl. 38 (1972), 205–207. Zbl 0225.54049, MR 0303368 |
Reference:
|
[14] Lan K., Webb J.: New fixed point theorems for a family of mappings and applications to problems on set with convex sections.Proc. Amer. Math. Soc. 126 (1998), 1127–1132. MR 1451816 |
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] Mehta G.: Fixed points, equilibria and maximal elements in linear topological spaces.Comment. Math. Univ. Carolin. 28 (1987), 377–385. Zbl 0632.47041, MR 0904761 |
Reference:
|
[17] Park S.: Generalized Fan-Browder fixed point theorems and their applications.In: Collection of Papers Dedicated to J. G. Park (1989), 164–176. MR 1183001 |
Reference:
|
[18] Sion M.: On general minimax theorems.Pacific J. Math. 8 (1958), 171–176. Zbl 0163.38203, MR 0097026 |
Reference:
|
[19] Tarafdar E.: On nonlinear variational variational inequalities.Proc. Amer. Math. Soc. 67 (1977), 95–98. MR 0467408 |
Reference:
|
[20] Wu X., Shen S.: A further generalization of Yannelis-Prabhakar’s continous selection theorem and its applications.J. Math. Anal. Appl. 197 (1996), 61–74. MR 1371276 |
Reference:
|
[21] Yannelis N. C., Prabhakar N. D.: Existence of maximal elements and equilibria in linear topological spaces.J. Math. Econom. 12 (1983), 233–245. Zbl 0536.90019, MR 0743037 |
. |