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Minimax problems of uniformly same-order set-valued mappings

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In this paper, a class of set-valued mappings is introduced, which is called uniformly same-order. For this sort of mappings, some minimax problems, in which the minimization and the maximization of set-valued mappings are taken in the sense of vector optimization, are investigated without any hypotheses of convexity.

Abstract

In this paper, a class of set-valued mappings is introduced, which is called uniformly same-order. For this sort of mappings, some minimax problems, in which the minimization and the maximization of set-valued mappings are taken in the sense of vector optimization, are investigated without any hypotheses of convexity.

참고문헌 (29)

  1. J. P. Aubin, "Applied Nonlinear Analysis" (1984), John Wiley and Sons
  2. J. P. Aubin, "Set-Valued Analysis" (1990), Birkhauser
  3. S. S. Chang, "Minimax inequalities for vector-valued mappings on W-spaces", J. Math. Anal. Appl, 198(2), pp.371~380 (1996)
  4. G. Y. Chen, "A generalized section theorem and a minimax inequality for a vector-valued mapping", Optimization, 22(5), pp.745~754 (1991)
  5. G. Y. Chen, "Ekeland’s "-variational principle for set-valued mappings", Math. Methods Oper. Res, 48(2), pp.181~186 (1998)
  6. G. Y. Chen, "Vector Optimization, Set-Valued and Variational Analysis" (2005), Springer
  7. Y. J. Cho, "Minimax theorems in probabilistic metric spaces", Bull. Austral. Math. Soc, 51(1), pp.103~119 (1995)
  8. Y. J. Cho, "Coincidence theorems and minimax inequalities in abstract convex spaces", J. Inequal. Appl, 126, pp.14~ (2011)
  9. K. Fan, "A minimax inequality and applications, In Inequalities, III", pp.103~113 (1972), Academic Press
  10. F. Ferro, "A minimax theorem for vector-valued functions", J. Optim. Theory Appl, 60(1), pp.19~31 (1989)
  11. X. H. Gong, "The strong minimax theorem and strong saddle points of vector-valued functions", Nonlinear Anal, 68(8), pp.2228~2241 (2008)
  12. J. Jahn, "Vector Optimization, Theory, Applications, and Extensions" (2004), Springer
  13. I. S. Kim, "Loose saddle points of set-valued maps in topological vector spaces", Appl. Math. Lett, 12(8), pp.21~26 (1999)
  14. W. K. Kim, "On a non-compact generalization of Fan’s minimax theorem", Taiwanese J. Math, 14(2), pp.347~358 (2010)
  15. G. Y. Li, "A note on nonconvex minimax theorem with separable homogeneous polynomials", J. Optim. Theory Appl, 150(1), pp.194~203 (2011)
  16. S. J. Li, "Minimax theorems for set-valued mappings", J. Optim. Theory Appl, 106(1), pp.183~200 (2000)
  17. X. B. Li, "A minimax theorem for vector valued functions in lexicographic order", Nonlinear Anal, 73(4), pp.1101~1108 (2010)
  18. L. J. Lin, "On vector quasi-saddle points of set-valued maps, In Generalized Convexity, Generalized Monotonicity and Applications", pp.311~319 (2005), Kluwer Academic Publishers
  19. D. T. Luc, "A saddlepoint theorem for set-valued maps", Nonlinear Anal, 18(1), pp.1~7 (1992)
  20. J. W. Nieuwenhuis, "Some minimax theorems in vector-valued functions", J. Optim. Theory Appl, 40(3), pp.463~475 (1983)
  21. S. Park, "The Fan minimax inequality implies the Nash equilibrium theorem", Appl. Math. Lett, 24(12), pp.2206~2210 (2011)
  22. D. S. Shi, "Minimax theorems and cone saddle points of uniformly same- order vector-valued functions", J. Optim. Theory Appl, 84(3), pp.575~587 (1995)
  23. K. K. Tan, "Existence theorems for saddle points of vector-valued maps", J. Optim. Theory Appl, 89(3), pp.731~747 (1996)
  24. T. Tanaka, "Some minimax problems of vector-valued functions", J. Optim. Theory Appl, 59(3), pp.505~524 (1988)
  25. M. G. Yang, "Minimax theorems for vector-valued mappings in abstract convex spaces", Taiwanese J. Math, 14(2), pp.719~732 (2010)
  26. Z. Yang, "Generalized Browder-type fixed point theorem with strongly geo- desic convexity on Hadamard manifolds with applications", Indian J. Pure Appl. Math, 43(2), pp.129~144 (2012)
  27. Q. B. Zhang, "Generalized saddle points theorems for set- valued mappings in locally generalized convex spaces", Nonlinear Anal, 71(1), pp.212~218 (2009)
  28. Y. Zhang, "Ky Fan minimax inequalities for set-valued mappings", Fixed Point Theory Appl, 64, pp.12~ (2012)
  29. Y. Zhang, "Minimax problems for set-valued mappings", Numer. Funct. Anal. Optim, 33(2), pp.239~253 (2012)

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