Taiwanese Journal of Mathematics


Haishu Lu and Jihui Zhang

Full-text: Open access


In this paper, we found a new result by relaxing the condition of [15, Corollary 2]. As its application, we have obtained some new minimax inequalities of Ky Fan and minimax theorems in the spaces without linear structure.

Article information

Taiwanese J. Math., Volume 8, Number 4 (2004), 703-712.

First available in Project Euclid: 18 July 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 49A29 49J35: Minimax problems

minimax theorems $H$-spaces $H$-convex upper (lower) semicontinuous set-valued mapping


Lu, Haishu; Zhang, Jihui. MINIMAX INEQUALITIES IN THE SPACES WITHOUT LINEAR STRUCTURE. Taiwanese J. Math. 8 (2004), no. 4, 703--712. doi:10.11650/twjm/1500407713. https://projecteuclid.org/euclid.twjm/1500407713

Export citation


  • [1.] C. W. Ha, Minimax and fixed point theorems, Math. Ann. 248 (1980), 73-77.
  • [2.] C. W. Ha, On a minimax inequality of Ky Fan, Proc. Amer. Math. Soc. 99 (1987), 680-682.
  • [3.] K. Fan, Some properties of convex sets relation to fixed point theorems, Math. Ann. 266 (1984), 519-537.
  • [4.] A. Granas and F. C. Liu, Coincidence for set-valued maps and minimax inequalities, J. Math. Pure. Appl. 65 (1986), 119-148.
  • [5.] K. K. Tan, Comparison theorems on minimax inequalities, variational inequalities, J. London. Math. Soc. 28 (1983), 555-562.
  • [6.] S. Kum, A generalization of generalized quasivariational inequalities, J. Math. Anal. Appl. 182 (1994), 158-164.
  • [7.] J. Y. Fu, Implict variational inequalities for multivalued mappings, J. Math. Anal. Appl. 189 (1995), 801-814.
  • [8.] K. Fan, A generalization of Tychonoff's fixed theorem, Math. Ann. 142 (1961), 305-310.
  • [9.] C. Horvath, Point fixes et coincidences pour les applicatios multivoques sans convexite, C. R. Acad. Sci. Paris. 296 (1983), 403-406.
  • [10.] C. Horvath, Point fixes et coincidences dans les espaces topologiques compacts contractiles, C. R. Acad. Sci. Paris. 299 (1984), 519-521.
  • [11.] C. Horvath, Some results on multivalued mappings and inequalities without convexity, in “Nonlinear and Convex Analysis” (B. L. Lin and S. Simons, Eds.), Marcel Dekker. New York, 1987, pp. 99-106.
  • [12.] E. Tarafdar, Fixed point theorems in $H$-spaces and equilibrium points of abstract economies, J. Austral. Math. Soc. 53 (1992), 252-260.
  • [13.] S. Park, J. S. Bae and H. K. Kang, Geometric properties minimax inequalities, and fixed point theorems on convex spaces, Proc. Amer. Math. Soc. 121 (1994), 429-439.
  • [14.] C. Berge, Topological Spaces, Oliver and Boyd, Edinburgh, London, 1963.
  • [15.] X. Wu and F. Li, On Ky Fan's Section Theorem, J. Math. Anal. Appl. 227 (1998), 112-121.
  • [16.] J. H. Zhang, Minimax inequalities of Ky Fan, Appl. Math. Lett. 11 (1998), 37-41.
  • [17.] J. F. McClendon, Minimax and variational inequalities for compact spaces, Proc. Amer. Math. Soc. 89 717-721, (1983).