• Title/Summary/Keyword: locally convex space

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FIXED POINTS OF BETTER ADMISSIBLE MAPS ON GENERALIZED CONVEX SPACES

  • Park, Se-Hie
    • Journal of the Korean Mathematical Society
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    • v.37 no.6
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    • pp.885-899
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    • 2000
  • We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

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Best Approximation Result in Locally Convex Space

  • Nashine, Hemant Kumar
    • Kyungpook Mathematical Journal
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    • v.46 no.3
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    • pp.389-397
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    • 2006
  • A fixed point theorem of Singh and Singh [10] is generalized to locally convex spaces and the new result is applied to extend a result on invariant approximation of Jungck and Sessa [5].

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CLOSED CONVEX SPACELIKE HYPERSURFACES IN LOCALLY SYMMETRIC LORENTZ SPACES

  • Sun, Zhongyang
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.6
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    • pp.2001-2011
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    • 2017
  • In 1997, H. Li [12] proposed a conjecture: if $M^n(n{\geqslant}3)$ is a complete spacelike hypersurface in de Sitter space $S^{n+1}_1(1)$ with constant normalized scalar curvature R satisfying $\frac{n-2}{n}{\leqslant}R{\leqslant}1$, then is $M^n$ totally umbilical? Recently, F. E. C. Camargo et al. ([5]) partially proved the conjecture. In this paper, from a different viewpoint, we study closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ and also prove that $M^n$ is totally umbilical if the square of length of second fundamental form of the closed convex spacelike hypersurface $M^n$ is constant, i.e., Theorem 1. On the other hand, we obtain that if the sectional curvature of the closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ satisfies $K(M^n)$ > 0, then $M^n$ is totally umbilical, i.e., Theorem 2.

FIXED POINTS OF NONEXPANSIVE MAPS ON LOCALLY CONVEX SPACES

  • Ling, Joseph M.
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.1
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    • pp.21-36
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    • 2000
  • In this article we study the relation between subinvariant submean and normal structure in a locally convex topological vector space. This extends in a natural way a result obtained recently by Lau and Takahashi. Our approach also follows closely theirs.

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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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FIXED POINT THEOREMS, SECTION PROPERTIES AND MINIMAX INEQUALITIES ON K-G-CONVEX SPACES

  • Balaj, Mircea
    • Journal of the Korean Mathematical Society
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    • v.39 no.3
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    • pp.387-395
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    • 2002
  • In [11] Kim obtained fixed point theorems for maps defined on some “locally G-convex”subsets of a generalized convex space. Theorem 2 in Kim's article determines us to introduce, in this paper, the notion of K-G-convex space. In this framework we obtain fixed point theorems, section properties and minimax inequalities.