Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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NEW MAXIMUM THEOREMS WITH STRICT QUASI-CONCAVITY

  • Kim, Won-Kyu (INSTITUTE OF SCIENCE EDUCATION, CHUNGBUK NATIONAL UNIVERSITY) ;
  • Yoon, Ju-Han (INSTITUTE OF SCIENCE EDUCATION, CHUNGBUK NATIONAL UNIVERSITY)
  • Published : 2001.08.01
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Abstract

In this paper, we first rove the strict quasi-concavity of maximizing function, and next prove a new maximum theorem using Fan’s generalization of the classical KKM theorem. Also an existence theorem of social equilibrium can be proved when an additional assumption on the constraint correspondence is assumed. Finally, we give illustrative two examples of constrained optimization problems.

Keywords

References

  1. Mathematical Methods of Game and Economic Theory J.-P. Aubin
  2. Espaces Topologiques et Fonctions Multivoques C. Berge
  3. Fixed Point Theorems with Applications to Economics and Game Theory K. C. Border
  4. Proc. Nat. Acad. Sci. v.38 A social equilibrium existence theorem G. Debrue
  5. J. Econom. Theory v.25 Nine kinds of quasiconcavity and concavity W. E. Diewert;M. Avriel;I. Zang
  6. Math. Ann. v.142 A generalization of Tychonoff's fixed point theorem K. Fan
  7. The Scotish Book KKM-maps and their applications to nonlinear problems A. Granas;R. D. Mauldin(ed.)
  8. J. Korean Math. Soc. v.35 A new minimum theorem and its applications W. K. Kim;D. I. Rim;S. M. Im
  9. Econom. Lett. v.15 A generalization of the maximum theorem W. Leininger
  10. Aequationes Math. v.33 On midpoint convex set-valued functions K. Nikodem
  11. Appl. Math. Lett. v.11 Remarks on a social equilibrium existence theorem of G. Debreu S. Park
  12. J. Math. Econom v.24 Transfer continuities, generalization of the Weierstrass and maximum theorems: a full characterization G. Tian;J. Zhou
  13. Internat. Econom. Rev. v.20 A generalization of the maximum theorem M. Walker