대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제15권2호
  • /
  • Pages.197-231
  • /
  • 2000
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

일반화 볼록공간에서의 평형문제들

  • 박세희 (서울대학교 자연과학대학 수학과)
  • 발행 : 2000.04.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

평형문제들에서의 기본적인 정리들이 일반화 볼록공간에서 어떻게 확장되는가를 보인다. KKM 이론의 중요한 정리들 대부분이 위상벡터공간에서의 선형성을 가정하지 않아도 위상적인 성질만으로 성립한다. 이같은 정리들의 예로는 KKM정리, von Neumann의 최소최대정리와 교차정리, Nash의 평형정리, 여러 가지 부동점정리, 극대원정리, Ky Fan의 최소최대부등식, 변분부등식들, 최량근사정리, 일반화 의사평형문제들의 해의 존재정리들이 있다.

키워드

참고문헌

  1. Combinatorial Topology P. S. Alexandroff
  2. Topologie I P. Alexandroff;H. Hopf
  3. J. Math. Econom v.3 Existence of equlibrium actions and of equilibrium A. Borglin;H. Keiding
  4. Math. Student v.63 From optimization and variational inequalities to equilibrium problems E. Blum;W. Oettl
  5. Math. Ann v.177 The fixed point theory of multi-valued mappings in topological vector spaces F. E. Browder
  6. Math. Ann v.142 A generalization of Tychonoff's fixed point theorem Ky Fan
  7. Math. Ann v.163 Applications of a theorem concerning sets with convex sections Ky Fan
  8. Math. Z v.112 Extensions of two fixed point theorems of F. E. Browder Ky Fan
  9. Inequalities III A minimax inequality and applications Ky Fan;O. Shisha(ed.)
  10. Game Theory and Mathematical Economics A further generalization of Shapley's generalization of the Knaster-Kuratowski-Mazurkiewicz theorem Ky Fan;O. Moeschlin(eds.);D. Palaschke(eds.)
  11. Math. Ann v.266 Some properties of convex sets related to fixed point theorems Ky Fan
  12. The Scottish Book KKM maps and their applications to nonlinear problems A. Granas;R. D. Mauldin(ed.)
  13. Acta Math v.115 On some nonlinear elliptic differential functional equations P. Hartman;G. Stampacchia
  14. J. Math. Anal. Appl. v.38 Fixed points of compact multifunctions C. J. Himmelberg
  15. Nolinear Analysis and Convex Analysis Some results on multivalued mappings and inequalities without convexity C. D. Horvath;B. L. Lin(eds.);S. Simons(eds.)
  16. Methods Topologiques en Analyse Convexe, Sem. Math. Super 110 Convexite generalisee et applications C. D. Horvath
  17. J. Math. Anal. Appl v.156 Contractibility and general convexity C. D. Horvath
  18. Ann. Fac. Sci. Toulouse v.2 Extensions and selection theorems in topological spaces with a generalized convexity structure C. D. Horvath
  19. Duke Math. J v.8 A generalization of Brouwer fixed point theorem S. Kakutani
  20. J. Math. Anal. Appl v.121 Some applications of the Kakutani fixed point theorem W. K. Kim
  21. Math. Ann v.141 Leray-Schauder theory without local convexity V. Klee
  22. Fund. Math v.14 Ein Beweis des Fixpunktsatzes fur n-Dimensionale Simplexe B. Knaster;K. Kuratowski;und S. Mazurkiewicz
  23. J. Math. Anal. Appl v.97 On the use of KKM multifuntions in fixed point theory and related topics M. Lassonde
  24. C. R. Acad. Sci. Paris v.310 Sur le principe KKM M. Lassonde
  25. Discuss. Math.-Diff. Incl v.18 Coincidence theorems for set-valued maps with G-KKM property on generalized convex spaces L.-J. Lin;C.-J. Ko;S. Park
  26. Le Matematiche v.49 On general nonlinear complementarity problems and quasi-equilibria M. A. Noor;W. Oettli
  27. Numer. Funct. Anal. and Optimiz v.9 On generalizations of Ky Fan's theorems on best approximations Sehie Park
  28. Bull. Korean Math. Soc v.24 Some approximations of solutions of the Lions-Stampacchia variational inequality Sehie Park;J. A. Park
  29. Collec. of Papers Dedicated to J. G. Park Generalized Fan-Browder fixed point theorems and their applications Sehie Park
  30. J. Math. Anal. Appl v.141 Gneralizations of Ky Fan's matching theorems and their applications Sehie Park
  31. Bull. Korean Math. Soc v.26 Nonlinear variational inequalities and fixed point theorems Sehie Park;I. Kim
  32. Bull. Korean Math. Soc v.27 Convex spaces and KKM families of subsets Sehie Park
  33. Bull. Korean Math. Sco v.27 Convex spaces and KKM families of subsets Sehie Park
  34. Numer. Funct. Anal. and Optimiz v.11 Generalized matching theorems for closed converings of convex sets Sehie Park
  35. J. Korean Math. Soc v.28 Variational inequalities and extremal principles Sehie Park
  36. Progress in Approximation Theory Best approximations, inward sets, and fixed points Sehie Park;P. Nevai(eds.);A. Pinkus
  37. Bull. Korean Math. Soc v.28 Remarks on some variational inequalities Sehie Park
  38. J. Korean Math. Soc v.28 Generalizations of Ky Fan's matching theorems and their applications, II Sehie Park
  39. Fixed Point Theory and Applications Some coincidence theorems on acyclic multifunctions and applications to KKM theory Sehie Park;K.-K. Tan(ed.)
  40. Lecture Note Ser v.3 Some coincidence theorems on acyclic multifunctions and applications to KKM theory, II World Scientific Publ. River Edge
  41. Kyungpook Math. J. Amer. Math. Soc. Abstract 93T-47-15 v.32 On the KKM type theorems on spaces having certain contractible subsets Sehie Park
  42. Bull. Austral. Math. Soc. Amer. Math. Soc. Abstract 93T-47-45 v.47 On minimax inequalities on spaces having certain contractible subsets Sehie Park
  43. Proc. Coll. Natur. Sci. SNU v.18 Admissible classes of multifunctions on generalized convex spaces Sehie Park;H. Kim
  44. Proc. 2nd GARC Symp. Pure Appl. Math Generalization of the Prolla type best approximations in normed vector spaces Sehie Park;K. S. Jeong
  45. Numer. Funct. Anal. and Optimiz v.15 A unified approach to generalizations of the KKM type theorems related to acyclic maps Sehie Park
  46. Proc. Amer. Math. Soc. Amer. Math. Soc. Abstract 887-47-39 v.121 Geometric properties, minimax inequalities, and fixed point theorems on convex spaces Sehie Park;J. S. Bae;H. K. Kang
  47. Honam Math. J v.16 Remarks on generalizations of best approximation theorems Sehie Park
  48. J. Korean Math. Soc v.31 Foundatons of the KKM theory via coincidences of composites of admissible u.s.c. maps Sehie Park
  49. Indian J. pure appl. Math v.25 Remarks on best approximation theorems Sehie Park;S. P. Singh;B. Watson
  50. Nonlinear Analysis, TMA. Amer. Soc. Abstract 92T-47-162 v.24 Acyclic maps, minimax inequalities, and fixed points Sehie Park
  51. Bull. Austral. Math. Soc v.51 Best approximation theorems for composites of upper semicontinuous maps Sehie Park
  52. Kangweon-Kyungki Math J v.3 Some existence theorems for two variable functions on topological vector spaces Sehie Park
  53. Comment. Math v.36 Coincidence points and maximal elements of multifunctions on convexspaces Sehie Park
  54. Antipodal Points and Fixed Points. Lect. Notes Ser v.28 Eighty years of the Brouwer fixed point theorem Sehie Park
  55. Topology-Proc. in honor of J. Kim Some applications of the KKM theory and fixed point theory for admissible multifunctions Sehie Park
  56. Far East J. Math. Sci v.3 Generalized quasi-variational inequalities Sehie Park;M.-P. Chen
  57. J. Math. Anal. Appl v.197 Coincidence theorems for admissible umltifunctions on generalized convex spaces Sehie Park;H. Kim
  58. Kyungpook Math. J v.35 Remarks on set-valued generalizations of best approximation theorems Sehie Park
  59. Proc. Nonlinear Funct. Anal. and Appl v.1 Applications of the Idzik fixed point theorem Sehie Park
  60. ibid v.2 Corrections Sehie Park
  61. Colloq. Math v.71 The Idzik type quasi-variational inequalities and noncompact optimization problems Sehie Park;J. A. Park
  62. Nonlinear Analysis Forum v.2 Five episodes related to the Fan-Browder fixed point theorem Sehie Park
  63. Comm. Appl. Nonlinear Anal. Amer. Math. Soc. Abstract 97T-47-108 v.4 A unified approach to generalized quasi-variational inequalities Sehie Park;M.-P. Chen
  64. J. Math. Anal. Appl v.209 Foundations of the KKM theory on generalized convex spaces Sehie Park;H. Kim
  65. J. Korean Math. Soc v.34 A generalized minimax inequality related to admissible multimaps and its applications Sehie Park
  66. Numer. Funct. Anal. and Optimiz v.18 Best approximations and fixed points of nonexpansive maps in Hilbert spaces Sehie Park
  67. Indian J. Math v.39 On the Browder type best approximation theorems Sehie Park;M.-P. Chen
  68. J. Optim. Th. Appl v.95 Generalized equilibrium problems and generalized complementarity problems Sehie Park
  69. Math. Sci. Res. Hot-Line v.1 no.9 Fixed points of the better admissible multimaps Sehie Park
  70. Inter. J. Math. & Math. Sci. Amer. Math. Soc. Abstract 94T-47-163 v.20 Extensions of best approximation and coincidence theorems Sehie Park
  71. Math. Sci. Res. Hot-Line v.1 no.11 Collectively fixed points and equilibrium points of abstract economies Sehie Park
  72. Nonlinear Analysis, Amer. Math. Soc. Abstract 97T-47-150 v.31 Generalized variational inequalities and fixed point theorems Sehie Park;B. G. Kang
  73. J. Inequal & Appl v.2 Generalized variational inequalities of the Hartman-Stampacchia-Browder type Sehie Park;M.-P. Chen
  74. J. Math. Anal. Appl v.218 An application of Browder-type fixed point theorem to generalized variational inequalities Sehie Park;S. Kim
  75. Indian J. pure appl. Math v.29 Generalizations of the KKM type theorems on generalized convex spaces Sehie Park;H. Kim
  76. Differential Inclusions and Optimal Control, Lect. Notes in Nonlinear Anal v.2 Leray-Schauder type theorems and equilibrium existence theorems Sehie Park;A. Idzik
  77. J. Math. Anal. Appl. Amer. Math. Soc. Abstract 918-47-935 v.223 Approximation and fixed point theorems for condensing composites of multifunctions Sehie Park;T.-C. Lin
  78. Nonlinear Analysis v.33 A unified approach to variational inequalities on compact convex sets Sehie Park;M.-P. Chen
  79. J. Math. Anal. Appl v.224 On some generalized quasi-equilibrium problems Sehie Park;L.-J. Lin
  80. Appl. Math. Lett v.11 no.5 Remarks on a social equilibrium existence theorems of G. Debreu Sehie Park
  81. Comm. Appl. Nonlinear Anal v.5 Best approximations of 1-set-contractions in Banach spaces Sehie Park;J.-J. Lee
  82. Inter. J. Math & Math. Sci v.21 A general vector-valued variational inequality and tis fuzzy extension Sehie Park;B. S. Lee;G. M. Lee
  83. Acta Math. Hungarica v.81 Fixed point theorems for new classes of multimaps Sehie Park
  84. Nonlinear Analysis and Convex Analysis(Proc. NACA'98, Niigata, Japan, July 28-31, 1998) Remarks on a fixedpoint problem of Ben-El-Mechaiekh Sehie Park
  85. Josai Math. Monograph v.1 Minimax theorems and the Nash equilibria on generalized convex spaces Sehie Park
  86. J. Math. Anal. Appl v.233 Remarks on fixed points, maximal elements and equilibria of generalized games Sehie Park;L.-J. Lin;Z.-T. Yu
  87. J. Korean Math. Soc v.36 Coincidence theorems in a product of generalized convex spaces and applications to equilibria Sehie Park;H. Kim
  88. Commun. Appl. Nonlinear Anal v.6 Best approximations and fixed points of multimap whose domains and ranges have different topologies Sehie Park;M.-P. Chen
  89. Numer. Funct. Anal. and Optimiz v.25 Continuous selection theorems in generalized convex spaces Sehie Park
  90. Vietnam J. Math v.27 Ninety years of the Brouwer fixed point theorem Sehie Park
  91. Newsletter Korean Math. Soc v.65 Recent unification in the analytical fixed point theory Sehie Park
  92. Korean J. Comp. Appl. Math v.7 Elements of the KKM theory for generalized convex spaces Sehie Park
  93. Appl. Math. Lett v.13 Remarks on saddle points in nonconvex sets Sehie Park;I.-S. Kim
  94. J. Comp. Appl. Math v.113 Acyclic versions of the von Neumann and Nash equilibrium theorems Sehie Park
  95. Progress of Math v.32 Abstract Sehie Park
  96. Bull. Korean Math. Soc v.37 Coincidence and saddle point theorems on generalized convex spaces Sehie Park;I.-S. Kim
  97. Math. Comp. Modelling. AMer. Math. Soc. Abstract 97T-47-107 Fixed points and quasi-equilibrium problems Sehie Park
  98. Proc. Internat. Conf. on Math. Anal. and Appl v.1-A New subclasses of generalized convex spaces Sehie Park
  99. Proc. Internat. Conf. on Math. Anal. and Appl v.1-A Remarks on fixed point theorems for generalized convex spaces Sehie Park
  100. Novi Sad J. Math. Minimax theorems in convex spaces Sehie Park
  101. Inter. J. Math. & Math. Sci v.23 Fixed points. intersection theorems, variational inequalities, and equilibrium theorems Sehie Park
  102. J. Inequal. & Appl Saddle point theorems on generalized convex spaces Sehie Park;I.-S. Kim
  103. Nonlinear Analysis Fixed point theorems in locally G-convex spaces Sehie Park
  104. Remarks on generalized quasi-equilibrium problems Sehie Park;M. P. Chen;L. -J. Lin
  105. Taiwan. J. Math Fixed point and non-retract theorems-Classical circular tours Sehie Park;K.-S. Jeong
  106. Remarks on topologies of generalized convex spaces Sehie Park
  107. A unified theory on generalized KKM maps in generalized convex spaces Sehie Park
  108. Nonlinear and Convex Analysis(Proc. in honor of Ky Fan) Covering theorems of convex sets related to fixed-point theorems M.-H. Shin;K.-K. Tan
  109. Pacific J. Math v.8 On general minimax theorems M. Sion
  110. Proc. WCNA'96, Nonlinear Anal. TMA v.30 G-KKM theorem, minimax inequalities and saddle points K.-K. Tan
  111. Proc. Nonlinear Funct. Anal. and Appl v.1 Fixed point theorems on G-convex spaces and applications K.-K. Tan;X.-L. Zhang
  112. J. Math. Anal. Appl v.170 Generalization of FKKM theorem and the Ky Fan minimax inequality with applications to maximal elements, price equilibrium and complementarity G. Q. Tian
  113. Math. Ann v.100 Zur Theorie der Gesellschaftsspiele J. von Neumann
  114. Ergeb. eines Math. Kolloq v.8 Uber ein Okonomisches Gleichungssystem and eine Verallgemeinerung des Brouwerschen Fixpunktsatzes Sehie Park
  115. Review of Econ. Studies v.13 A model of general economic equilibrium Sehie Park
  116. J. Math. Economics v.12 Existence of maximal elements and equilibria in linear topological spaces N. Yannelis;N. Prabhakar
  117. Nonliner Functional Analysis and Its Applications v.5 E. Zeidler