Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-24T11:25:30.067Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimax inequalities in G-convex spaces

Published online by Cambridge University Press:  17 April 2009

Mircea Balaj
Mircea Balaj
Affiliation:
Department of Mathematics, University of Oradea, 410087, Oradea, Romania, e-mail: mbalaj@uoradea.ro
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we establish two minimax theorems of Sion-type in G-convex spaces. As applications we obtain generalisations of some theorems concerning compatibility of some systems of inequalities.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 3 , June 2005 , pp. 367 - 376
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Chang, T.H. and Yen, C.L., ‘KKM property and fixed point theorems’, J. Math. Anal. Appl. 203 (1996), 224–235.CrossRefGoogle Scholar
[2]Ding, X.P., ‘New H-KKM theorems and equilibria of generalized games’, Indian J.Pure Appl. Math. 27 (1996), 1057–1071.Google Scholar
[3]Fan, K., ‘Minimax theorems’, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 42–47.CrossRefGoogle ScholarPubMed
[4]Fan, K., ‘Sur un théorème minimax’, C. R. Acad. Sci. Paris Ser. I. Math. 259 (1964), 3925–3928.Google Scholar
[5]Granas, A. and Liu, F.-C., ‘Remark on a theorem of Ky Fan concerning systems of inequalities’, Bull. Inst. Math. Acad. Sinica 11 (1983), 639–643.Google Scholar
[6]Granas, A. and Liu, F.-C., ‘Théorèmes de minimax’, C. R. Acad. Sci. Paris Ser. I. Math. 298 (1984)), 329–332.Google Scholar
[7]Granas, A. and Liu, F.-C., ‘Coincidences for set-valued maps and minimax inequalities’, J. Math. Pures Appl. 65 (1986), 119–148.Google Scholar
[8]Lin, L.J., ‘Application of a fixed point theorem in G-convex space’, Nonlinear Anal. 46 (2001), 601–608.CrossRefGoogle Scholar
[9]Lin, L.J., Ko, C.J. and Park, S., ‘Coincidence theorems for set-valued maps with G-KKM property a nd fixed point theorems’, Discuss. Math. Differential Incl. 18 (1998), 69–85.Google Scholar
[10]Lin, L.J. and Park, S., ‘On some generalized quasi-equilibrium problems’, J. Math. Anal. Appl. 224 (1998), 167–181.CrossRefGoogle Scholar
[11]Liu, F.-C., ‘A note on the von Neumann-Sion minimax principle’, Bull. Inst. Math. Acad. Sinica 6 (1978), 517–524.Google Scholar
[12]Park, S., ‘Foundations of the KKM theory on generalized convex spaces’, J. Math. Anal. Appl. 209 (1997), 551–571.CrossRefGoogle Scholar
[13]Park, S., ‘Continuous selection theorems in generalized convex spaces’, Numer. Funct. Anal. Optimi. 20 (1999), 567–583.CrossRefGoogle Scholar
[14]Park, S., ‘Elements of the KKM theory for generalized convex spaces’, Korean J. Comput. Appl. Math. 7 (2000), 1–28.CrossRefGoogle Scholar
[15]Park, S., ‘New subclasses of generalized convex spaces’, in Fixed point theory and applications, (Cho, Y.J., Editor) (Nova Sci. Publ., New York, 2000), pp. 91–98.Google Scholar
[16]Park, S., ‘Remarks on fixed point theorems for generalized convex spaces’, in Fixed point theory and applications, (Cho, Y.J., Editor) (Nova Sci. Publ., New York, 2000), pp. 135–144.Google Scholar
[17]Yu, Z.T. and Lin, L.J., ‘Continuous selection and fixed point theorems’, Nonlinear Anal. 52 (2003), 445–455.CrossRefGoogle Scholar
[18]Wu, X. and Shen, S., ‘A further generalization of Yannelis-Prabhakar's continuous selection theorem and its applications’, J. Math. Anal. Appl. 197 (1996), 61–74.CrossRefGoogle Scholar