×

Some properties of convex sets related to fixed point theorems. (English) Zbl 0515.47029


MSC:

47H10 Fixed-point theorems
46A55 Convex sets in topological linear spaces; Choquet theory
49J40 Variational inequalities
PDFBibTeX XMLCite
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
[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 · Zbl 1308.49002
[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
[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
[13] Fan, K.: A generalization of Tychonoffs fixed point theorem. Math. Ann.142, 305-310 (1961) · Zbl 0093.36701
[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
[16] Fan, K.: Extensions of two fixed point theorems of F. E. Browder. Math. Z.112, 234-240 (1969) · Zbl 0185.39503
[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
[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
[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
[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
[30] Kakutani, S.: A generalization of Brouwer’s fixed-point theorem. Duke Math. J.8, 457-459 (1941) · Zbl 0061.40304
[31] Knaster, B., Kuratowski, C., Mazurkiewicz, S.: Ein Beweis des Fixpunktsatzes fürn-dimensionale Simplexe. Fund. Math.14, 132-137 (1929) · JFM 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
[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
[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
[37] von Neumann, J.: Zur Theorie der Gesellschaftsspiele. Math. Ann.100, 295-320 (1928) · JFM 54.0543.02
[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
[41] Tarafdar, E., Thompson, H.B.: On Ky Fan’s minimax principle. J. Austral. Math. Soc. Ser. A26, 220-226 (1978) · Zbl 0401.47027
[42] Tychonoff, A.: Ein Fixpunktsatz. Math. Ann.111, 767-776 (1935) · Zbl 0012.30803
[43] Yen, C.L.: A minimax inequality and its applications to variational inequalities. Pac. J. Math.97, 477-481 (1981) · Zbl 0493.49009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.