Admissible maps, intersection results, coincidence theorems
Balaj, Mircea
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 753-762 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2001-01-01
Classification:  47H10,  54C60,  54H25 
@article{119290,
     author = {Mircea Balaj},
     title = {Admissible maps, intersection results, coincidence theorems},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {753-762},
     zbl = {1068.47068},
     mrnumber = {1883383},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119290}
}

Balaj, Mircea. Admissible maps, intersection results, coincidence theorems. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 753-762. http://gdmltest.u-ga.fr/item/119290/

Allen G. Variational inequalities, complementary problems and duality theorems, J. Math. Anal. Appl. 58 (1977), 1-10. (1977) | MR 0513305

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

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. (1982)

Browder F.E. The fixed point theory of multi-valued mappings in topological vector spaces, Math. Ann. 177 (1968), 283-301. (1968) | MR 0229101 | Zbl 0176.45204

Chang S.Y. A generalization of KKM principle and its applications, Soochow J. Math. 15 (1989), 7-17. (1989) | MR 1025967 | Zbl 0747.47033

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. (1990) | MR 1054086 | Zbl 0709.47053

Fan K. A generalization of Tychonoff's fixed point theorem, Math. Ann 142 (1961), 305-310. (1961) | MR 0131268 | Zbl 0093.36701

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

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. | MR 0556363 | Zbl 0432.54040

Fan K. Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519-537. (1984) | MR 0735533 | Zbl 0515.47029

Gorniewicz L. A Lefschetz-type fixed point theorem, Fund. Math. 88 (1975), 103-115. (1975) | MR 0391062 | Zbl 0306.55007

Gorniewicz L. Homological methods in fixed point theory of multi-valued maps, Dissertationes Math. 129 (1976), 1-71. (1976) | MR 0394637 | Zbl 0324.55002

Ha C.-W. Minimax and fixed point theorems, Math. Ann. 248 (1980), 73-77. (1980) | MR 0569411 | Zbl 0413.47042

Kim W.K. Some applications of the Kakutani fixed point theorem, J. Math. Anal. Appl. 121 (1987), 119-122. (1987) | MR 0869523 | Zbl 0612.54055

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

Lassonde M. Sur le principle KKM, C.R. Acad. Sci. Paris 310 (1990), 573-576. (1990) | MR 1050134

Lin T.-C. Convex sets, fixed points, variational and minimax inequalities, Bull. Austral. Math. Soc. (Ser. A) 34 (1986), 107-117. (1986) | MR 0847978 | Zbl 0597.47038

Park S. Generalizations of Ky Fan's matching theorems and their applications, J. Math. Anal. Appl. 141 (1989), 164-176. (1989) | MR 1004591 | Zbl 0681.47028

Park S. Convex spaces and KKM families of subsets, Bull. Korean Math. Soc. 27 (1990), 11-14. (1990) | MR 1060811 | Zbl 0746.47036

Park S. Generalizations of Ky Fan's matching theorems and their applications, $II$, J. Korean Math. Soc. 28 (1991), 275-283. (1991) | MR 1127832 | Zbl 0813.47063

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

Park S. Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps, J. Korean Math. Soc. 31 (1994), 493-519. (1994) | MR 1297433 | Zbl 0829.49002

Park S. Ninety years of the Browder fixed point theorem, Vietnam J. Math. 27 (1999), 193-232. (1999) | MR 1811334

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. (1995) | MR 1338994 | Zbl 0868.54015

Sehgal V.M.; Singh S.P.; Whitfield J.H.M. KKM-maps and fixed point theorems, Indian J. Math. 32 (1990), 289-296. (1990) | MR 1088610

Shih M.-H. Covering properties of convex sets, Bull. London Math. Soc. 18 ((1986)), 57-59. ((1986)) | MR 0841369 | Zbl 0579.52004

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. | MR 0892795 | Zbl 0637.47029

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. (1988) | MR 0951575 | Zbl 0664.52001

Shioji N. A further generalization of the Knaster-Kuratowski-Mazurkiewicz theorems, Proc. Amer. Math. Soc. 111 (1991), 187-195. (1991) | MR 1045601

Takahashi W. Nonlinear variational inequalities and fixed point theorems, J. Math. Soc. Japan 28 (1976), 168-181. (1976) | MR 0399979 | Zbl 0314.47032

Tarafdar E. On nonlinear variational inequalities, Proc. Amer. Math. Soc. 67 (1977), 95-98. (1977) | MR 0467408 | Zbl 0369.47029

Tarafdar E. On minimax principles and sets with convex sections, Publ. Math. Debrecen 29 (1982), 219-226. (1982) | MR 0678897 | Zbl 0536.47038