zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Some properties of convex sets related to fixed point theorems. (English) Zbl 0515.47029

MSC:
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
46A55Convex sets in topological linear spaces; Choquet theory
49J40Variational methods including variational inequalities
WorldCat.org
Full Text: DOI EuDML
References:
[1] Allen, G.: Variational inequalities, complementarity problems, and duality theorems. J. Math. Anal. Appl.58, 1-10 (1977) · Zbl 0383.49005 · doi:10.1016/0022-247X(77)90222-0
[2] Aubin, J.P.: Applied functional analysis. New York: Wiley-Interscience 1979 · Zbl 0424.46001
[3] Aubin, J.P.: Mathematical methods of game and economic theory. Amsterdam: North-Holland 1979 · Zbl 0452.90093
[4] Baiocchi, C., Capelo, A.: Disequazioni variazionali e quasivariazionali. Applicazioni a problemi di frontiera libera, Vol. 2: Problemi quasivariazionali. Bologna: Pitagora. 1978
[5] Ben-El-Mechaiekh, H., Deguire, P., Granas, A.: Une alternative non-linéaire en analyse convexe et applications. C.R. Acad. Sci. Paris Sér. I Math.295, 257-259 (1982) · Zbl 0521.47027
[6] Ben-El-Mechaiekh, H., Deguire, P., Granas, A.: Points fixes et coincidences pour les applications multivoques (applications de Ky Fan). C.R. Acad. Sci. Paris Sér. I Math.295, 337-340 (1982) · Zbl 0525.47042
[7] Ben-El-Mechaiekh, H., Deguire, P., Granas, A.: Points fixes et coincidences pour les fonctions multivoques II. (Applications de type ? et ?*). C.R. Acad. Sci. Paris Sér. I Math.295, 381-384 (1982) · Zbl 0525.47043
[8] Brézis, H., Nirenberg, L., Stampacchia, G.: A remark on Ky Fan’s minimax principle. Boll. Un. Mat. Ital.6, 293-300 (1972) · Zbl 0264.49013
[9] Browder, F.E.: The fixed point theory of multi-valued mappings in topological vector spaces. Math. Ann.177, 283-301 (1968) · Zbl 0176.45204 · doi:10.1007/BF01350721
[10] Dugundji, J., Granas, A.: KKM maps and variational inequalities. Ann. Scuola Norm. Sup. Pisa Cl. Sci.5, 679-682 (1978) · Zbl 0396.47037
[11] Dugundji, J., Granas, A.: Fixed point theory, Vol. 1. Monografie Matematyczne61, Warszawa, 1982 · Zbl 0483.47038
[12] Fan, K.: Fixed-point and minimax theorems in locally convex topological linear spaces. Proc. Nat. Acad. Sci. USA38, 121-126 (1952) · Zbl 0047.35103 · doi:10.1073/pnas.38.2.121
[13] Fan, K.: A generalization of Tychonoffs fixed point theorem. Math. Ann.142, 305-310 (1961) · Zbl 0093.36701 · doi:10.1007/BF01353421
[14] Fan, K.: Sur un théorème minimax. C.R. Acad. Sci. Paris Groupe 1,259, 3925-3928 (1964) · Zbl 0138.37304
[15] Fan, K.: Applications of a theorem concerning sets with convex sections. Math. Ann.163, 189-203 (1966) · Zbl 0138.37401 · doi:10.1007/BF02052284
[16] Fan, K.: Extensions of two fixed point theorems of F. E. Browder. Math. Z.112, 234-240 (1969) · Zbl 0185.39503 · doi:10.1007/BF01110225
[17] Fan, K.: A minimax inequality and applications. In: Inequalities, Vol. III, pp. 103-113. (Ed. O. Shisha). New York, London: Academic Press, 1972 · Zbl 0302.49019
[18] Fan, K.: Fixed-point and related theorems for non-compact convex sets. In: Game theory and related topics, pp. 151-156. (Eds. O. Moeschlin, D. Pallaschke). Amsterdam: North-Holland, 1979
[19] Fan, K.: A further generalization of Shapley’s generalization of the Knaster-Kuratowski-Mazurkiewicz theorem. In: Game theory and mathematical economics, pp. 275-279. (Eds. O. Moeschlin, D. Pallaschke). Amsterdam: North-Holland, 1981
[20] Glicksberg, I.L.: A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points. Proc. Am. Math. Soc.3, 170-174 (1952) · Zbl 0046.12103
[21] Granas, A.: KKM-maps and their applications to nonlinear problems. In: The Scottish Book (Mathematics from the Scottish Café), pp. 45-61. (Ed. R. D. Mauldin). Basel, Boston: Birkhäuser, 1982
[22] Gwinner, J.: Nichtlineare Variationsungleichungen mit Anwendungen. Frankfurt: Haag-Herchen, 1978 · Zbl 0393.49001
[23] Gwinner, J.: On fixed points and variational inequalities?A circular tour. Nonlinear Anal.5, 565-583 (1981) · Zbl 0461.47037 · doi:10.1016/0362-546X(81)90104-8
[24] Ha, C.W.: A non-compact minimax theorem. Pac. J. Math.97, 115-117 (1981) · Zbl 0474.49015
[25] Halpern, B.R., Bergman, G.M.: A fixed-point theorem for inward and outward maps. Trans. Am. Math. Soc.130, 353-358 (1968) · Zbl 0153.45602 · doi:10.1090/S0002-9947-1968-0221345-0
[26] Horvath, C.: Points fixes et coincidences pour les applications multivoques sans convexité. C.R. Acad. Sci. Paris Sér. I. Math.296, 403-406 (1983) · Zbl 0527.54042
[27] Horvath, C.: Points fixes et coincidences sans convexité. Thèse Ph. D. Univ. de Montréal, 1983 · Zbl 0527.54042
[28] Ichiishi, T.: On the Knaster-Kuratowski-Mazurkiewicz-Shapley theorem. J. Math. Anal. Appl.81, 297-299 (1981) · Zbl 0475.90094 · doi:10.1016/0022-247X(81)90063-9
[29] Joly, J.L., Mosco, U.: A propos de l’existence et de la régularité des solutions de certaines inéquations quasi-variationnelles. J. Functional Analysis34, 107-137 (1979) · Zbl 0425.49018 · doi:10.1016/0022-1236(79)90028-4
[30] Kakutani, S.: A generalization of Brouwer’s fixed-point theorem. Duke Math. J.8, 457-459 (1941) · Zbl 0061.40304 · doi:10.1215/S0012-7094-41-00838-4
[31] Knaster, B., Kuratowski, C., Mazurkiewicz, S.: Ein Beweis des Fixpunktsatzes fürn-dimensionale Simplexe. Fund. Math.14, 132-137 (1929) · Zbl 55.0972.01
[32] Lassonde, M.: On the use of KKM multifunctions in fixed point theory and related topics. J. Math. Anal. Appl.97, 151-201 (1983) · Zbl 0527.47037 · doi:10.1016/0022-247X(83)90244-5
[33] Liu, F.C.: A note on the von Neumann-Sion minimax principle. Bull. Inst. Math. Acad. Sinica6, 517-524 (1978) · Zbl 0421.46006
[34] Ma, T.W.: On sets with convex sections. J. Math. Anal. Appl.27, 413-416 (1969) · Zbl 0176.42703 · doi:10.1016/0022-247X(69)90058-4
[35] Mosco, U.: Implicit variational problems and quasi variational inequalities. In: Nonlinear operators and the calculus of variations. Lecture Notes in Math. 543, pp. 83-156. (Eds. J. P. Gossez, E. J. Lami Dozo, J. Mawhin, L. Waelbroeck). Berlin, Heidelberg, New York: Springer, 1976
[36] Nash, J.: Non-cooperative games. Ann. Math.54, 286-295 (1951) · Zbl 0045.08202 · doi:10.2307/1969529
[37] von Neumann, J.: Zur Theorie der Gesellschaftsspiele. Math. Ann.100, 295-320 (1928) · Zbl 54.0543.02 · doi:10.1007/BF01448847
[38] Shapley, L.S.: On balanced games without side payments. In: Mathematical programming, pp. 261-290. (Eds. T. C. Hu, S. M. Robinson). New York: Academic Press, 1973 · Zbl 0267.90100
[39] Sion, M.: On general minimax theorems. Pac. J. Math.8, 171-176 (1958) · Zbl 0081.11502
[40] Takahashi, W.: Nonlinear variational inequalities and fixed point theorems. J. Math. Soc. Japan28, 168-181 (1976) · Zbl 0314.47032 · doi:10.2969/jmsj/02810168
[41] Tarafdar, E., Thompson, H.B.: On Ky Fan’s minimax principle. J. Austral. Math. Soc. Ser. A26, 220-226 (1978) · Zbl 0401.47027 · doi:10.1017/S144678870001171X
[42] Tychonoff, A.: Ein Fixpunktsatz. Math. Ann.111, 767-776 (1935) · Zbl 0012.30803 · doi:10.1007/BF01472256
[43] Yen, C.L.: A minimax inequality and its applications to variational inequalities. Pac. J. Math.97, 477-481 (1981) · Zbl 0493.49009