Generalizations of the Fan-Browder fixed point theorem and minimax inequalities
Balaj, Mircea ; Muresan, Sorin
Archivum Mathematicum, Tome 041 (2005), p. 399-407 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 2005-01-01
Classification:  47H10,  49J35,  54C60,  54H25
@article{107969,
     author = {Mircea Balaj and Sorin Muresan},
     title = {Generalizations of the Fan-Browder fixed point theorem and minimax inequalities},
     journal = {Archivum Mathematicum},
     volume = {041},
     year = {2005},
     pages = {399-407},
     zbl = {1111.54032},
     mrnumber = {2195493},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107969}
}
Balaj, Mircea; Muresan, Sorin. Generalizations of the Fan-Browder fixed point theorem and minimax inequalities. Archivum Mathematicum, Tome 041 (2005) pp. 399-407. http://gdmltest.u-ga.fr/item/107969/

Balaj M. A variant of a fixed point theorem of Browder and some applications, Math. Montisnigri 9 (1998), 5–13. (1998) | MR 1657668 | Zbl 0999.47045

Balaj M. Applications of two matching theorems in generalized convex spaces, Nonlinear Anal. Forum 7 (2002), 123–130. | MR 1959938 | Zbl 1034.54016

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. (1982)

Browder F. E. The fixed point theory of multivalued mappings in topological vector spaces, Math. Ann. 177 (1968), 238–301. (1968) | MR 0229101

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). (1982) | MR 0737389

Deguire P. Browder-Fan fixed point theorem and related results, Discuss. Math. Differential Incl. 15 (1995), 149–162. (1995) | MR 1390397 | Zbl 0931.47041

Deguire P.; Lassonde M. Families sélectantes, Topol. Methods Nonlinear Anal. 5 (1995), 261–269. (1995) | MR 1374063

Ding X. P. New H-KKM theorems and equilibria of generalized games, Indian J. Pure Appl. Math. 27 (1996), 1057–1071. (1996) | MR 1420096

Ding X. P. A coincidence theorem involving contractible spaces, Appl. Math. Lett. 10 (1997), 53–56. (1997) | MR 1457639 | Zbl 0879.54055

Fan K. A generalization of Tichonoff’s fixed point theorems, Math. Ann. 142 (1961), 305–310. (1961) | MR 0131268

Fan K. Sur une théorème minimax, C.R. Acad. Sci. Paris 259 (1964), 3925–3928. (1964) | MR 0174955

Fan K. A minimax inequality and applications, In: Inequalities III (O. Shisha, ed.), pp. 103–113, Academic Press, New York, 1972. (1972) | MR 0341029 | Zbl 0302.49019

Himmelberg C. J. Fixed points of compact multifunctions, J. Math. Anal. Appl. 38 (1972), 205–207. (1972) | MR 0303368 | Zbl 0225.54049

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. (1998) | MR 1451816

Lassonde M. On the use of KKM multifunctions in fixed point theory and related topics, J. Math. Anal. Appl. 97 (1983), 151–201. (1983) | MR 0721236 | Zbl 0527.47037

Mehta G. Fixed points, equilibria and maximal elements in linear topological spaces, Comment. Math. Univ. Carolin. 28 (1987), 377–385. (1987) | MR 0904761 | Zbl 0632.47041

Park S. Generalized Fan-Browder fixed point theorems and their applications, In: Collection of Papers Dedicated to J. G. Park (1989), 164–176. (1989) | MR 1183001

Sion M. On general minimax theorems, Pacific J. Math. 8 (1958), 171–176. (1958) | MR 0097026 | Zbl 0163.38203

Tarafdar E. On nonlinear variational variational inequalities, Proc. Amer. Math. Soc. 67 (1977), 95–98. (1977) | MR 0467408

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. (197 ) | MR 1371276

Yannelis N. C.; Prabhakar N. D. Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econom. 12 (1983), 233–245. (1983) | MR 0743037 | Zbl 0536.90019