Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지

ON A VARIATIONAL INEQUALITY WITH $\mathcal{C}$-CONCAVITY

  • Kim, Won Kyu (Department of Mathematics Education, Chungbuk National University) ;
  • Lee, Kyoung Hee (Division of Liberal Arts, Korea University of Technology & Education)
  • Received : 2008.11.17
  • Accepted : 2009.02.17
  • Published : 2009.03.31
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Abstract

In this paper, using the diagonally $\mathcal{C}$-concave condition, we will prove a functional inequality in a topological space, and as an application, we can obtain a new variational inequality.

Keywords

Acknowledgement

Supported by : Chungbuk National University

References

  1. F. Browder, The fixed point theory of multi-valued mappings in topological vector spaces, Math. Ann. 177 (1968), 283-310. https://doi.org/10.1007/BF01350721
  2. K. Fan, Minimax theorems. Proc. Nat. Acad. Sci. U.S.A. 39(1953), 42 - 47. https://doi.org/10.1073/pnas.39.1.42
  3. K. Fan, A Minimax inequality and applications, In Inequalities III (Edited by O. Shisha) Proc. of 3rd Symposium on Inequalities, pp. 103-113, Academic Press, New York, 1972.
  4. F. Forgo, On the existence of Nash-equilibrium in n-person generalized concave games. In Generalized Convexity: Lecture Notes in Economics and Mathematical Systems, Vol. 405 (Edited by S. Komlosi, T. Rapcsak and S. Schaible), pp. 53-61, Springer-Verlag, Berlin, 1994.
  5. P. Hartman and G. Stampacchia, On some non-linear elliptic differential equations, Acta Math. 115 (1966), 271-310. https://doi.org/10.1007/BF02392210
  6. W. K. Kim and K. H. Lee, On the existence of Nash equilibrium in N-person games with C-concavity, Computers & Math. Appl. 44 (2002), 1219-1228. https://doi.org/10.1016/S0898-1221(02)00228-6
  7. S. Park, Elements of the KKM-theory for generalized convex spaces, Korean J. Comp. Appl. Math. 7 (2000), 1-28.
  8. W. Takahashi, Nonlinear variational inequalities and fixed point theorems, J. Math. Soc. Japan 28 (1976), 168-181. https://doi.org/10.2969/jmsj/02810168