Coincidence points and maximal elements of multifunctions on convex spaces
Park, Sehie
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 57-67 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 1995-01-01
Classification:  47H04,  47H10,  49A40,  49J27,  49J40,  54C60,  54H25,  55M20
@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/

Ben-El-Mechaiekh H. The coincidence problem for compositions of set-valued maps, Bull. Austral. Math. Soc. 41 (1990), 421-434. (1990) | MR 1071044 | Zbl 0727.54019

Ben-El-Mechaiekh H.; Deguire P. Approximation of non-convex set-valued maps, C. R. Acad. Sci. Paris 312 (1991), 379-384. (1991) | MR 1096616 | Zbl 0719.54053

Ben-El-Mechaiekh H.; Deguire P. 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

Ben-El-Mechaiekh H.; Deguire P. Approachability and fixed points for non-convex set-valued maps, J. Math. Anal. Appl. 170 (1992), 477-500. (1992) | MR 1188567 | Zbl 0762.54033

Ben-El-Mechaiekh H.; Deguire P.; Granas A. 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

Bohnenblust H.F.; Karlin S. 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

Brouwer L.E.J. Über Abbildungen von Mannigfaltigkeiten, Math. Ann. 71 (1912), 97-115. (1912) | MR 1511644

Dzedzej Z. Fixed point index theory for a class of nonacyclic multivalued maps, Dissertationes Math. 253 (1985), 53pp. (1985) | MR 0839694 | Zbl 0592.55001

Ky Fan 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

Ky Fan A generalization of Tychonoff's fixed point theorems, Math. Ann. 142 (1961), 305-310. (1961) | MR 0131268

Ky Fan Sur un théorème minimax, C. R. Acad. Sci. Paris 259 (1964), 3925-3928. (1964) | MR 0174955 | Zbl 0138.37304

Glicksberg I.L. 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

Górniewicz L. Homological methods in fixed point theory of multivalued maps, Dissertationes Math. 129 (1976), 71pp. (1976) | MR 0394637

Granas A.; Liu F.-C. Coincidences for set-valued maps and minimax inequalities, J. Math. Pures et Appl. 65 (1986), 119-148. (1986) | MR 0867668 | Zbl 0659.49007

Ha C.-W. Extensions of two fixed point theorems of Ky Fan, Math. Z. 190 (1985), 13-16. (1985) | MR 0793344 | Zbl 0551.47024

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

Kakutani S. A generalization of Brouwer's fixed-point theorem, Duke Math. J. 8 (1941), 457-459. (1941) | MR 0004776 | Zbl 0061.40304

Kim W.K. Existence of maximal elements and equilibrium for a non-paracompact $N$-person game, Proc. Amer. Math. Soc. 116 (1992), 797-807. (1992) | MR 1123657

Kim W.K.; Tan K.-K. A variational inequality in non-compact sets and its applications, Bull. Austral. Math. Soc. 46 (1992), 139-148. (1992) | MR 1170448 | Zbl 0747.47037

Knaster B.; Kuratowski C.; Mazurkiewicz S. Ein Beweis des Fixpunktsatzes für $n$-dimensionale Simplexe, Fund. Math. 14 (1929), 132-137. (1929)

Lessonde M. 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

Levine N. A decomposition of continuity in topological spaces, Amer. Math. Monthly 68 (1961), 44-46. (1961) | MR 0126252 | Zbl 0100.18601

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

Mehta G. Weakly lower demicontinuous preference maps, Economics Letters 23 (1987), 15-18. (1987) | MR 0895251

Mehta G.; Sessa S. Coincidence theorems and maximal elements in topological vector spaces, Math. Japonica 37 (1992), 839-845. (1992) | MR 1186550 | Zbl 0763.47034

Michael E. A selection theorem, Proc. Amer. Math. Soc. 17 (1966), 1404-1406. (1966) | MR 0203702 | Zbl 0178.25902

Park Sehie Fixed point theory of multifunctions in topological vector spaces, J. Korean Math. Soc. 29 (1992), 191-208. (1992) | MR 1157308 | Zbl 0758.47048

Park Sehie Fixed point theory of multifunctions in topological vector spaces II, J. Korean Math. Soc. 30 (1993), 413-431. (1993) | MR 1239332 | Zbl 0797.47029

Park Sehie 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 Sehie Fixed points of acyclic maps on topological vector spaces, Proc. 1st World Congress of Nonlinear Analysts. | Zbl 0863.47042

Park S.; Bae J.S. On zeros and fixed points of multifunctions with non-compact convex domains, Comment. Math. Univ. Carolinae 34 (1993), 257-264. (1993) | MR 1241735

Park S.; Singh S.P.; Watson B. Some fixed point theorems for composites of acyclic maps, Proc. Amer. Math. Soc. 121 (1994), 1151-1158. (1994) | MR 1189547 | Zbl 0806.47053

Rim D.I.; Kim W.K. 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

Schauder J. Zur Theorie stetiger Abbildungen in Funktionalräumen, Math. Z. 26 (1927), 47-65. (1927) | MR 1544841

Schauder J. Der Fixpunktsatz in Funktionalräumen, Studia Math. 2 (1930), 171-180. (1930)

Sessa S. 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

Tarafdar E. 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

Tychonoff A. Ein Fixpunktsatz, Math. Ann. 111 (1935), 767-776. (1935) | MR 1513031 | Zbl 0012.30803

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