Taiwanese Journal of Mathematics


Gu-Sheng Tang, Cao-Zong Cheng, and Bor-Luh Lin

Full-text: Open access


In this paper, we generalize Ky Fan’s minimax inequality to vectorvalued function with values in a topological vector space acting on the product of two other topological vector spaces which are connected by another function. In these results, the concavity or convexity on a function is transferred to another function. And a sufficient condition for the existence of solution for a variational inclusion is given.

Article information

Taiwanese J. Math., Volume 13, Number 1 (2009), 239-251.

First available in Project Euclid: 18 July 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49K35: Minimax problems 52A30: Variants of convex sets (star-shaped, (m, n)-convex, etc.)

generalized Ky Fan's inequality set-valued monotone mapping variational inclusion


Tang, Gu-Sheng; Cheng, Cao-Zong; Lin, Bor-Luh. SOME GENERALIZED KY FAN’S INEQUALITIES. Taiwanese J. Math. 13 (2009), no. 1, 239--251. doi:10.11650/twjm/1500405281. https://projecteuclid.org/euclid.twjm/1500405281

Export citation


  • Ky Fan, A minimax inequality and its application, in: Inequalities, Vol. 3, Ed. O. Shisha, Academic press, New York, 1972, pp. 103-113.
  • M. A. Geraghty and Bor-Luh Lin, Minimax theorems without linear Structure, Linear and Multilinear Algebra, 17 (1985), 171-180.
  • Bor-Luh Lin and Xiu-Chi Quan, A noncompact topological theorem, J. Math. Anal. Appl., 161 (1991), 587-590.
  • Bor-Luh Lin and Xiu-Chi Quan, A symmetric minimax theorem without linear structure, Arch. Math., 52 (1989), 367-370.
  • S. Simons, Two-function minimax theorems and variational inequalities for functions on compact and noncompact sets, with some comments on fixed-point theorems, Proc. Symp. Pure. Math., 45 (1986), 377-392.
  • Shih-sen Chang, Xian Wu and Shu-wen Xiang, A topological KKM theorem and minimax theorems, J. Math. Anal. Appl., 182 (1994), 756-767.
  • D. Kurowa, Convexity for set-valued Maps, Appl. Math. Lett., 9 (1996), 97-101.
  • T. Tanaka, Some minimax problems of vector-valued functions, J. Opt. Theo. Appl., 59 (1988), 505-524.
  • T. Tanaka, Generalized quasiconvexities, cone saddle points, and minimax theorems for vector-valued functions, J. Opt. Theo. Appl., 81 (1994), 355-377.
  • A. Kristály and C. Varga, Set-valued versions of Ky Fan's inequality with application to variational inclusion theory, J. Math. Anal. Appl., 282 (2003), 8-20.
  • S. J. Li, G. Y. Chen and G. M. Lee, Minimax theorems for set-valued mappings, J. Opt. Theo. Appl., 106(1) (2000), 183-200.
  • S. J. Li, G. Y. Chen, K. L. Teo, and X. Q. Yang, Generalized minimax inequalities for set-valued mappings, J. Math. Anal. Appl., 281 (2003), 707-723.
  • J. P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, 1990.
  • C. Z. Cheng, A minimax inequality and variational inequalities, Progress in Natural Science, 7(1) (1997), 92-97.