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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 65, 2016 - Issue 5
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Articles

Minimax theorems for set-valued maps without continuity assumptions

Pages 957-976 | Received 18 Oct 2014, Accepted 27 Aug 2015, Published online: 07 Oct 2015

References

  • Fan K. Minimax theorems. Proc. Natl. Acad. Sci. U.S.A. 1953;39:42–47.
  • Fan K. A minimax inequality and applications. Inequalities III. New York (NY): Academic Press; 1972.
  • Fan K. Sur un théorème minimax [On a minimax theorem]. C. R. Acad. Sci. Paris. 1964;259:3925–3928.
  • Chbania Z, Riahi H. Weak and strong convergence of proximal penalization and proximal splitting algorithms for two-level hierarchical Ky Fan minimax inequalities. Optimization. 2015;64:1285–1303.
  • Chuang C-S, Lin L-J. New existence theorems for quasi-equilibrium problems and a minimax theorem on complete metric spaces. J. Glob. Optim. 2013;57:533–547.
  • Ferro F. A minimax theorem for vector-valued functions. J. Optim. Theory Appl. 1989;60:19–31.
  • Ferro F. A minimax theorem for vector-valued functions. J. Optim. Theory Appl. 1991;68:35–48.
  • Gavrea I, Trif T. On Ky Fan’s Inequality. Math. Inequal. Appl. 2001;4:223–230.
  • Georgiev PG, Tanaka T. Ky Fan’s inequality for set-valued maps with vector-valued images. Nonlinear analysis and convex analysis (Kyoto, 2000). S\={u}rikaisekikenky\={u}sho K\={o}ky\={u}roku. 2001;1187:143–154.
  • Jahn J. Vector optimization: theory, applications and extensions. Berlin: Springer; 2004.
  • Li SJ, Chen GY, Lee GM. Minimax theorems for set-valued mappings. J. Optim. Theory Appl. 2000;106:183–199.
  • Li SJ, Chen GY, Teo KL, et al. Generalized minimax inequalities for set-valued mappings. J. Math. Anal. Appl. 2003;281:707–723.
  • Nessah R, Tian G. Existence of solution of minimax inequalities, equilibria in games and fixed points without convexity and compactness assumptions. J. Optim. Theory Appl. 2013;157:75–95.
  • Nieuwenhuis JW. Some minimax theorems in vector-valued functions. J. Optim. Theory Appl. 1983;40:463–475.
  • Patriche M. Fixed point theorems and applications in theory of games. Fixed Point Theory. 2014;15:199–212.
  • Peng ZY, Yang XM. Semicontinuity of the solution mappings to weak generalized parametric Ky Fan inequality problems with trifunctions. Optimization. 2014;63:447–457.
  • Rooin J. On Ky Fan’s inequality and its additive analogues. Math. Inequal. Appl. 2003;6:595–604.
  • Sándor J, Trif T. A new refinement of the Ky Fan inequality. Math. Inequal. Appl. 1999;2:529–533.
  • Tanaka T. Some minimax problems of vector-valued functions. J. Optim. Theory Appl. 1998;59:505–524.
  • Tanaka T. Generalized quasiconvexities, cone saddle points and minimax theorems for vector-valued functions. J. Optim. Theory Appl. 1994;81:355–377.
  • Zhang Q, Cheng C, Li X. Generalized minimax theorems for two set-valued mappings. J. Ind. Man. Optim. 2013;9:1–12.
  • Zhang Y, Li SJ. Minimax theorems for scalar set-valued mappings with nonconvex domains and applications. J. Glob. Optim. 2013;57:1359–1373.
  • Zhang Y, Li SJ. Ky Fan minimax inequalities for set-valued mappings. Fixed Point Theory Appl. 2012;2012:64.
  • Zhang Y, Li SJ, Zhu SK. Minimax problems for set-valued mappings. Numer. Funct. Anal. Optim. 2012;33:239–253.
  • Kuroiowa D, Tanaka T, Ha TXD. On cone convexity of set-valued maps. Nonlinear Anal.: Theory Methods Appl. 1997;30:1487–1496.
  • Smajdor W. Set-valued quasiconvex functions and their constant selections. Functional equations and inequalities. Dordrecht: Kluwer Academic; 2000. p. 233–248.

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