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2003 | 23 | 1 | 5-19
Tytuł artykułu

Variational inequalities in noncompact nonconvex regions

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EN
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EN
In this paper, a general existence theorem on the generalized variational inequality problem GVI(T,C,ϕ) is derived by using our new versions of Nikaidô's coincidence theorem, for the case where the region C is noncompact and nonconvex, but merely is a nearly convex set. Equipped with a kind of V₀-Karamardian condition, this general existence theorem contains some existing ones as special cases. Based on a Saigal condition, we also modify the main theorem to obtain another existence theorem on GVI(T,C,ϕ), which generalizes a result of Fang and Peterson.
Twórcy
  • Center for General Education, National Taipei University of Technology, Taipei, Taiwan, Republic of China
autor
  • Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, Republic of China
Bibliografia
  • [1] E.G. Begle, Locally connected spaces and generalized manifolds, Amer. Math. J. 64 (1942), 553-574.
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  • [3] E.G. Begle, A fixed point theorem, Ann. Math. 51 (1950), 544-550.
  • [4] F.E. Browder, Coincidence theorems, minimax theorems, and variational inequalities, Contemp. Math. 26 (1984), 67-80.
  • [5] D. Chan and J.S. Pang, The generalized quasi-variational inequality problem, Math. Oper. Res. 7 (1982), 211-222.
  • [6] L.J. Chu and C.Y. Lin, New versions of Nikaidô's coincidence theorem, Discuss. Math. DICO 22 (2002), 79-95.
  • [7] S.C. Fang and E.L. Peterson, Generalized variational inequalities, J. Optim. Th. Appl. 38 (3) (1982), 363-383.
  • [8] H. Halkin, Finite convexity in infinite-dimensional spaces, Proc. of the Colloquium on Convexity, Copenhagen (1965), W. Fenchel (ed.), Copenhagen (1967), 126-131.
  • [9] G. Isac, Complementarity problems, Lecture Notes in Math. 1528, Springer-Verlag, New York, (1992).
  • [10] S. Karamardian, The complementarity problem, Math. Program. 2 (1972), 107-129.
  • [11] B. Knaster, C. Kuratowski and S. Mazurkiewicz, Ein beweis des fixpunktsatzes fur n-dimensionale simplexe, Fundamenta Math. 14 (1929) 132-137.
  • [12] L.J. Lin, Pre-Vector variational inequalities, Bull. Australian Math. Soc. 53 (1995), 63-70.
  • [13] G.J. Minty, On the maximal domain of a monotone function, Michigan Math. J. 8 (1961), 135-137.
  • [14] H. Nikaidô, Coincidence and some systems of inequalities, J. Math. Soc., Japan 11 (1959), 354-373.
  • [15] R.T. Rockafellar, On the virtual convexity of the domain and range of a nonlinear maximal monotone operator, Math. Ann. 185 (1970), 81-90.
  • [16] R. Saigal, Extension of the generalized complemetarity problem, Math. of Oper. Res. 1 (3) (1976), 260-266.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1042
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