Generalized and unified versions of coincidence or maximal element theorems of Fan, Yannelis and Prabhakar, Ha, Sessa, Tarafdar, Rim and Kim, Mehta and Sessa, Kim and Tan are obtained. Our arguments are based on our recent works on a broad class of multifunctions containing composites of acyclic maps defined on convex subsets of Hausdorff topological vector spaces.
@article{118732, author = {Sehie Park}, title = {Coincidence points and maximal elements of multifunctions on convex spaces}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {36}, year = {1995}, pages = {57-67}, zbl = {0829.47050}, mrnumber = {1334414}, language = {en}, url = {http://dml.mathdoc.fr/item/118732} }
Park, Sehie. Coincidence points and maximal elements of multifunctions on convex spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 57-67. http://gdmltest.u-ga.fr/item/118732/
The coincidence problem for compositions of set-valued maps, Bull. Austral. Math. Soc. 41 (1990), 421-434. (1990) | MR 1071044 | Zbl 0727.54019
Approximation of non-convex set-valued maps, C. R. Acad. Sci. Paris 312 (1991), 379-384. (1991) | MR 1096616 | Zbl 0719.54053
General fixed point theorems for non-convex set-valued maps, C. R. Acad. Sci. Paris 312 (1991), 433-438. (1991) | MR 1096627 | Zbl 0795.47036
Approachability and fixed points for non-convex set-valued maps, J. Math. Anal. Appl. 170 (1992), 477-500. (1992) | MR 1188567 | Zbl 0762.54033
Points fixes et coincidences pour les fonctions multivoques, II (Applications de type $\varphi$ et $\varphi^*$), C. R. Acad. Sci. Paris 295 (1982), 381-384. (1982) | MR 0684731
On a theorem of Ville, in ``Contributions to the Theory of Games," Ann. of Math. Studies, No.24, pp.155-160, Princeton Univ. Press, 1950. | MR 0041415 | Zbl 0041.25701
Über Abbildungen von Mannigfaltigkeiten, Math. Ann. 71 (1912), 97-115. (1912) | MR 1511644
Fixed point index theory for a class of nonacyclic multivalued maps, Dissertationes Math. 253 (1985), 53pp. (1985) | MR 0839694 | Zbl 0592.55001
Fixed-point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 121-126. (1952) | MR 0047317 | Zbl 0047.35103
A generalization of Tychonoff's fixed point theorems, Math. Ann. 142 (1961), 305-310. (1961) | MR 0131268
Sur un théorème minimax, C. R. Acad. Sci. Paris 259 (1964), 3925-3928. (1964) | MR 0174955 | Zbl 0138.37304
A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points, Proc. Amer. Math. Soc. 3 (1952), 170-174. (1952) | MR 0046638 | Zbl 0163.38301
Homological methods in fixed point theory of multivalued maps, Dissertationes Math. 129 (1976), 71pp. (1976) | MR 0394637
Coincidences for set-valued maps and minimax inequalities, J. Math. Pures et Appl. 65 (1986), 119-148. (1986) | MR 0867668 | Zbl 0659.49007
Extensions of two fixed point theorems of Ky Fan, Math. Z. 190 (1985), 13-16. (1985) | MR 0793344 | Zbl 0551.47024
Fixed points of compact multifunctions, J. Math. Anal. Appl. 38 (1972), 205-207. (1972) | MR 0303368 | Zbl 0225.54049
A generalization of Brouwer's fixed-point theorem, Duke Math. J. 8 (1941), 457-459. (1941) | MR 0004776 | Zbl 0061.40304
Existence of maximal elements and equilibrium for a non-paracompact $N$-person game, Proc. Amer. Math. Soc. 116 (1992), 797-807. (1992) | MR 1123657
A variational inequality in non-compact sets and its applications, Bull. Austral. Math. Soc. 46 (1992), 139-148. (1992) | MR 1170448 | Zbl 0747.47037
Ein Beweis des Fixpunktsatzes für $n$-dimensionale Simplexe, Fund. Math. 14 (1929), 132-137. (1929)
Réduction du cas multivoque au cas univoque dans les problèmes de coïncidence, in ``Fixed Point Theory and Applications'' (M.A. Théra and J.-B. Baillon, Eds.), pp.293-302, Longman Scientific & Technical, Essex, 1991. | MR 1122836
A decomposition of continuity in topological spaces, Amer. Math. Monthly 68 (1961), 44-46. (1961) | MR 0126252 | Zbl 0100.18601
Fixed points, equilibria and maximal elements in linear topological spaces, Comment. Math. Univ. Carolinae 28 (1987), 377-385. (1987) | MR 0904761 | Zbl 0632.47041
Weakly lower demicontinuous preference maps, Economics Letters 23 (1987), 15-18. (1987) | MR 0895251
Coincidence theorems and maximal elements in topological vector spaces, Math. Japonica 37 (1992), 839-845. (1992) | MR 1186550 | Zbl 0763.47034
A selection theorem, Proc. Amer. Math. Soc. 17 (1966), 1404-1406. (1966) | MR 0203702 | Zbl 0178.25902
Fixed point theory of multifunctions in topological vector spaces, J. Korean Math. Soc. 29 (1992), 191-208. (1992) | MR 1157308 | Zbl 0758.47048
Fixed point theory of multifunctions in topological vector spaces II, J. Korean Math. Soc. 30 (1993), 413-431. (1993) | MR 1239332 | Zbl 0797.47029
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
Fixed points of acyclic maps on topological vector spaces, Proc. 1st World Congress of Nonlinear Analysts. | Zbl 0863.47042
On zeros and fixed points of multifunctions with non-compact convex domains, Comment. Math. Univ. Carolinae 34 (1993), 257-264. (1993) | MR 1241735
Some fixed point theorems for composites of acyclic maps, Proc. Amer. Math. Soc. 121 (1994), 1151-1158. (1994) | MR 1189547 | Zbl 0806.47053
A fixed point theorem and existence of equilibrium for abstract economies, Bull. Austral. Math. Soc. 45 (1992), 385-394. (1992) | MR 1165145 | Zbl 0745.90015
Zur Theorie stetiger Abbildungen in Funktionalräumen, Math. Z. 26 (1927), 47-65. (1927) | MR 1544841
Der Fixpunktsatz in Funktionalräumen, Studia Math. 2 (1930), 171-180. (1930)
Some remarks and applications of an extension of a lemma of Ky Fan, Comment. Math. Univ. Carolinae 29 (1988), 567-575. (1988) | MR 0972839 | Zbl 0674.47041
An extension of Fan's fixed point theorem and equilibrium point of an abstract economy, Comment. Math. Univ. Carolinae 31 (1990), 723-730. (1990) | MR 1091369 | Zbl 0745.47046
Ein Fixpunktsatz, Math. Ann. 111 (1935), 767-776. (1935) | MR 1513031 | Zbl 0012.30803
Existence of maximal elements and equilibria in linear topological spaces, J. Math. Economics 12 (1983), 233-245. (1983) | MR 0743037 | Zbl 0536.90019