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Existence theorems for maximal elements in H-spaces with applications on the minimax inequalities and equilibrium of games

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Języki publikacji
EN
Abstrakty
EN
In this paper, we give two new existence theorems for maximal elements in H-spaces. As their applications, we obtain a extended version of Fan-Yen minimax inequality and some new existence theorems of an equilibrium for a qualitative game and an abstract economy. Our main results not only generalize the corresponding results of [4, 12, 15, 16] to H -spaces, but also the open question raised by Yannelis and Prabhakar [15] is answered in affirmative.
Wydawca
Rocznik
Strony
283--293
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • Department of Mathematics Yunnan Normal University Kunming Yunnan 650092 P. R. China
Bibliografia
  • [1] Borglin, A. and Keiding, H., Existence of equilibrium actions and of equilibrium: A note on the new existence theorem, J. Math. Econom. 3 (1976), 313-316.
  • [2] Cubiotti, P., Some remarks on fixed points of lower semicontinuous multifunctions, J. Math. Anal. Appl. 174 (1993), 407-412.
  • [3] Ding, X. P., Kim, W. K. and Tan, K. K., Equilibria of generalized games with L- majorized correspondences, Internat. J. Math. Math. Sci. 17(4) (1994), 783-790.
  • [4] Fan, K., A minimax theorems and applications. Inequalities III, Ed. O. Shisha, Academic Press, New York, 1972, 103-113.
  • [5] Gajek. L. and Zagrodny, D., Existence of maximal points with respect to ordered bipreference relations, J. Optim. Theory Appl. 70(2) (1991), 355-364.
  • [6] Gajek, L. and Zagrodny, D., Countably orderable sets and their applications in optimization, Optimization 26 (1992), 187-301.
  • [7] Gajek, L. and Zagrodny, D., Fixed-point theorems related to a general multiobjective optimization problem, Scient. Bull, of Lodz Technical University, Matematyka 25 (1993), 51-69.
  • [8] Himmelberg, C. J., Fixed points of compact multifunctions, J. Math. Anal. Appl. 38 (1972), 205-207.
  • [9] Michael, E., A theorem on semi-continuous set-valued functions, Duke Math. J. 26 (1959), 647-651.
  • [10] Michael, E., Continuous selections, I, Ann. of Math. 63 (1956), 361-382.
  • [11] Tan, K. K. and Yuan, X. Z., Some minimax inequalities and applications to existence of equilibria in H-spaces, Nonlinear Anal. 24(10) (1995), 1457-1470.
  • [12] Tan, K. K. and Yuan, X. Z., Existence of equilibrium for abstract economies, J. Math. Econom. 23 (1994), 243-251.
  • [13] Tarafdar, E., Fixed point theorems in H-spaces and equilibrium points of abstract economies, J. Austral. Math. Soc. Ser. B 53 (1992), 252-260.
  • [14] Tian, G., Fixed point theorems for mappings with noncompact and nonconvex domains, J. Math. Anal. Appl. 158 (1991), 161-167.
  • [15] Yannelis, N. C. and Prabhakar, N. D., Existence of maximal elements and equilibra in linear topological spaces, J. Math. Econom. 12 (1983), 223-245.
  • [16] Yen, C. L., A minimax inequality and its applications to variational inequalities, Pacific J. Math. 97 (1981), 477-481.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0013-0017
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