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INCLUSION AND INTERSECTION THEOREMS WITH APPLICATIONS IN EQUILIBRIUM THEORY IN G-CONVEX SPACES

Donal O'Regan|Mircea Balaj
대한수학회 (The Korean Mathematical Society)|2010.09|대한수학회지 (Journal of the KMS)|제47권 제5호|pp. 1017-1029

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키워드

fixed pointequilibrium problemsG-convex spacethe better admissible class
주제분류수학

초록

In this paper we obtain a very general theorem of ｐ-compatibility for three multivalued mappings, one of them from the class B. More exactly, we show that given a G-convex space Y , two topological spaces X and Z, a (binary) relation ｐ on 2Z and three mappings P : X ( Z,-Q : Y - Z and T ∈ B(Y,X) satisfying a set of conditions we can find (x, y) ∈ X ×Y such that x ∈ T(y) and P(ex)½ Q(ey). Two particular cases of this general result will be then used to establish existence theorems for the solutions of some general equilibrium problems.

Abstract

In this paper we obtain a very general theorem of ｐ-compatibility for three multivalued mappings, one of them from the class B. More exactly, we show that given a G-convex space Y , two topological spaces X and Z, a (binary) relation ｐ on 2Z and three mappings P : X ( Z,-Q : Y - Z and T ∈ B(Y,X) satisfying a set of conditions we can find (x, y) ∈ X ×Y such that x ∈ T(y) and P(ex)½ Q(ey). Two particular cases of this general result will be then used to establish existence theorems for the solutions of some general equilibrium problems.

참고문헌 (31)

  1. Q. H. Ansari, "A generalization of vectorial equilibria", Math. Methods Oper. Res., 46(2), pp.147~152 (1997)
  2. Q. H. Ansari, "System of vector equilibrium problems and its applications", J. Optim. Theory Appl., 107(3), pp.547~557 (2000)
  3. M. Balaj, "An intersection theorem with applications in minimax theory and equilibrium problem", J. Math. Anal. Appl., 336(1), pp.363~371 (2007)
  4. M. Balaj, "Coincidence and maximal element theorems and their applications to generalized equilibrium problems and minimax inequalities", Nonlinear Anal., 68(12), pp.3962~3971 (2008)
  5. M. Balaj, "Weak-equilibrium problems in G-convex spaces", Rend. Circ. Mat. Palermo, 57(1), pp.103~117 (2008)
  6. H. Ben-El-Mechaiekh, "Abstract convexity and fixed points", J. Math. Anal. Appl., 222(1), pp.138~150 (1998)
  7. T.-H. Chang, "KKM property and fixed point theorems", J. Math. Anal. Appl., 203(1), pp.224~235 (1996)
  8. X. P. Ding, "Genralized KKM type theorems in FC-spaces with applications", I, J. Global Optim., 36(4), pp.581~596 (2006)
  9. X. P. Ding, "Generalized KKM type theorems in FC-spaces with applications. II", J. Global Optim., 38(3), pp.367~385 (2007)
  10. X. P. Ding, "KKM type theorems and generalized vector equilibrium problems in noncompact FC-spaces", J. Math. Anal. Appl., 331(2), pp.1230~1245 (2007)
  11. X. P. Ding, "Fixed points and generalized vector equilibrium problems in generalized convex spaces", Indian J. Pure Appl. Math., 34(6), pp.973~990 (2003)
  12. X. P. Ding, "Generalized vector equilibrium problems in generalized convex spaces", J. Optim. Theory Appl., 120(2), pp.327~353 (2004)
  13. M. Fakhar, "Generalized vector equilibrium problems for pseudomonotone multivalued bifunctions", J. Optim. Theory Appl., 126(1), pp.109~124 (2005)
  14. M. Fang, "KKM type theorems with applications to generalized vector equilibrium problems in FC-spaces", Nonlinear Anal., 67(3), pp.809~817 (2007)
  15. J. Y. Fu, "Generalized vector quasi-equilibrium problems", Math. Methods Oper. Res., 52(1), pp.57~64 (2000)
  16. M. Lassonde, "Fixed points for Kakutani factorizable multifunctions", J. Math. Anal. Appl., 152(1), pp.46~60 (1990)
  17. L. J. Lin, "Geometric properties and coincidence theorems with applications to generalized vector equilibrium problems", J. Optim. Theory Appl., 117(1), pp.121~137 (2003)
  18. L. J. Lin, "The study of KKM theorems with applications to vector equilibrium problems with implicit vector variational inequalities problems", J. Global Optim., 32(1), pp.135~157 (2005)
  19. L. J. Lin, "Systems of equilibrium problems with applications to generalized Ekeland’s variational principle and systems of semi-infinite problems", J. Global Optim. (2007)
  20. L. J. Lin, "KKM type theorems and coincidence theorems with applications to the existence of equilibria", J. Optim. Theory Appl., 123(1), pp.105~122 (2004)
  21. L. J. Lin, "Existence of equilibria for multivalued mappings and its application to vectorial equilibria", J. Optim. Theory Appl., 114(1), pp.189~208 (2002)
  22. Z. D. Mitrovic, "On scalar equilibrium problem in generalized convex spaces", J. Math. Anal. Appl., 330(1), pp.451~461 (2007)
  23. S. Park, "Fixed points of the better admissible multimaps", Msath. Sci. Res. Hot-Line, 1(9), pp.1~6 (1997)
  24. S. Park, "Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps", J. Korean Math. Soc., 31(3), pp.493~519 (1994)
  25. S. Park, "Fixed points of better admissible maps on generalized convex spaces", J. Korean Math. Soc., 37(6), pp.885~899 (2000)
  26. S. Park, "New subclasses of generalized convex spaces, Fixed point theory and applications (Chinju, 1998)", pp.91~98 (2000), Nova Sci. Publ.
  27. S. Park, "Remarks on fixed point theorems for generalized convex spaces, Fixed point theory and applications (Chinju, 1998)", pp.135~144 (2000), Nova Sci. Publ.
  28. S. Park, "Fixed point theorems in locally G-convex spaces", Nonlinear Anal. Ser. A: Theory Methods, 48(6), pp.869~879 (2002)
  29. S. Park, "Remarks on equilibria for g-monotone maps on generalized convex spaces", J. Math. Anal. Appl., 269(1), pp.244~255 (2002)
  30. S. Park, "Admissible classes of multifunctions on generalized convex spaces", Proc. Coll. Natur. Sci., 통권 : 18, pp.1~21 (1993), Seoul National University
  31. N. X. Tan, "On the existence of equilibrium points of vector functions", Numer. Funct. Anal. Optim., 19(1), pp.141~156 (1998)

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