• Title/Summary/Keyword: intersection theorem.

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GENERALIZATIONS OF THE NASH EQUILIBRIUM THEOREM ON GENERALIZED CONVEX SPACES

  • Park, Se-Hie
    • Journal of the Korean Mathematical Society
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    • v.38 no.4
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    • pp.697-709
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    • 2001
  • Generalized forms of the von neumann-Sion type minimax theorem, the Fan-Ma intersection theorem, the Fan-a type analytic alternative, and the Nash-Ma equilibrium theorem hold for generalized convex spaces without having any linear structure.

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GENERALIZED MINIMAX THEOREMS IN GENERALIZED CONVEX SPACES

  • Kim, Hoon-Joo
    • Honam Mathematical Journal
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    • v.31 no.4
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    • pp.559-578
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    • 2009
  • In this work, we obtain intersection theorem, analytic alternative and von Neumann type minimax theorem in G-convex spaces. We also generalize Ky Fan minimax inequality to acyclic versions in G-convex spaces. The result is applied to formulate acyclic versions of other minimax results, a theorem of systems of inequalities and analytic alternative.

A NON-COMPACT GENERALIZATION OF HORVATH'S INTERSECTION THEOREM$^*$

  • Kim, Won-Kyu
    • Bulletin of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.153-162
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    • 1995
  • Ky Fan's minimax inequality is an important tool in nonlinear functional analysis and its applications, e.g. game theory and economic theory. Since Fan gave his minimax inequality in [2], various extensions of this interesting result have been obtained (see [4,11] and the references therein). Using Fan's minimax inequality, Ha [6] obtained a non-compact version of Sion's minimax theorem in topological vector spaces, and next Geraghty-Lin [3], Granas-Liu [4], Shih-Tan [11], Simons [12], Lin-Quan [10], Park-Bae-Kang [17], Bae-Kim-Tan [1] further generalize Fan's minimax theorem in more general settings. In [9], using the concept of submaximum, Komiya proved a topological minimax theorem which also generalized Sion's minimax theorem and another minimax theorem of Ha in [5] without using linear structures. And next Lin-Quan [10] further generalizes his result to two function versions and non-compact topological settings.

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A STRUCTURE THEOREM FOR A CLASS OF GORENSTEIN IDEALS OF GRADE FOUR

  • Cho, Yong S.
    • Honam Mathematical Journal
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    • v.36 no.2
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    • pp.387-398
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    • 2014
  • In this paper, we give a structure theorem for a class of Gorenstein ideal of grade 4 which is the sum of an almost complete intersection of grade 3 and a Gorenstein ideal of grade 3 geometrically linked by a regular sequence. We also present the Hilbert function of a Gorenstein ideal of grade 4 induced by a Gorenstein matrix f.

FIXED POINT THEOREMS ON GENERALIZED CONVEX SPACES

  • Kim, Hoon-Joo
    • Journal of the Korean Mathematical Society
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    • v.35 no.2
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    • pp.491-502
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    • 1998
  • We obtain new fixed point theorems on maps defined on "locally G-convex" subsets of a generalized convex spaces. Our first theorem is a Schauder-Tychonoff type generalization of the Brouwer fixed point theorem for a G-convex space, and the second main result is a fixed point theorem for the Kakutani maps. Our results extend many known generalizations of the Brouwer theorem, and are based on the Knaster-Kuratowski-Mazurkiewicz theorem. From these results, we deduce new results on collectively fixed points, intersection theorems for sets with convex sections and quasi-equilibrium theorems.

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VANISHING THEOREM ON SINGULAR MODULI SPACES

  • Cho, Yong-Seung;Hong, Yoon-Hi
    • Journal of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.1069-1099
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    • 1996
  • Let X be a smooth, simply connected and oriented closed fourmanifold such that the dimension $b_{2}^{+}(X)$ of a maximal positive subspace for the intersection form is greater than or equal to 3.

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The essential point spectrum of a regular operator

  • Lee, Woo-Young;Lee, Hong-Youl;Han, Young-Min
    • Bulletin of the Korean Mathematical Society
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    • v.29 no.2
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    • pp.295-300
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    • 1992
  • In [5] it was shown that if T .mem. L(X) is regular on a Banach space X, with finite dimensional intersection T$^{-1}$ (0).cap.T(X) and if S .mem. L(X) is invertible, commute with T and has sufficiently small norm then T - S in upper semi-Fredholm, and hence essentially one-one, in the sense that the null space of T - S is finite dimensional ([4] Theorem 2; [5] Theorem 2). In this note we extend this result to incomplete normed space.

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