• 제목/요약/키워드: Hausdorff topological vector space

검색결과 9건 처리시간 0.021초

ON THE LOWER SEMICONTINUITY OF THE SOLUTION SETS FOR PARAMETRIC GENERALIZED VECTOR MIXED QUASIVARIATIONAL INEQUALITY PROBLEMS

  • HUNG, NGUYEN VAN
    • 대한수학회보
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    • 제52권6호
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    • pp.1777-1795
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    • 2015
  • In this paper, we establish sufficient conditions for the solution set of parametric generalized vector mixed quasivariational inequality problem to have the semicontinuities such as the inner-openness, lower semicontinuity and Hausdorff lower semicontinuity. Moreover, a key assumption is introduced by virtue of a parametric gap function by using a nonlinear scalarization function. Then, by using the key assumption, we establish condition ($H_h$(${\gamma}_0$, ${\lambda}_0$, ${\mu}_0$)) is a sufficient and necessary condition for the Hausdorff lower semicontinuity, continuity and Hausdorff continuity of the solution set for this problem in Hausdorff topological vector spaces with the objective space being infinite dimensional. The results presented in this paper are different and extend from some main results in the literature.

A REMARK ON MULTI-VALUED GENERALIZED SYSTEM

  • Kum, Sangho
    • 충청수학회지
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    • 제24권2호
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    • pp.163-169
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    • 2011
  • Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single-valued bi-operator F. In this note, we aim at an extension of (GS) due to Kazmi and Khan [7] into a multi-valued circumstance. We consider a fairly general problem called the multi-valued quasi-generalized system (in short, MQGS). Based on the existence of 1-person game by Ding, Kim and Tan [5], we give a generalization of (GS) in the name of (MQGS) within the framework of Hausdorff topological vector spaces. As an application, we derive an existence result of the generalized vector quasi-variational inequality problem. This result leads to a multi-valued vector quasi-variational inequality extension of the strong vector variational inequality (SVVI) due to Fang and Huang [6] in a general Hausdorff topological vector space.

A Maximal Element of Condensing Multimaps

  • Kim, Won Kyu
    • 충청수학회지
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    • 제6권1호
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    • pp.59-64
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    • 1993
  • In this note, we shall give a maximal element existence theorem for condensing multimaps in a locally convex Hausdorff topological vector space.

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A UNIFIED FIXED POINT THEORY OF MULTIMAPS ON TOPOLOGICAL VECTOR SPACES

  • Park, Seh-Ie
    • 대한수학회지
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    • 제35권4호
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    • pp.803-829
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    • 1998
  • We give general fixed point theorems for compact multimaps in the "better" admissible class $B^{K}$ defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for $\Phi$-condensing maps. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.n.

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A Generalization of the Hyers-Ulam-Rassias Stability of the Pexiderized Quadratic Equations, II

  • Jun, Kil-Woung;Lee, Yang-Hi
    • Kyungpook Mathematical Journal
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    • 제47권1호
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    • pp.91-103
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    • 2007
  • In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder ${\varphi}$ is defined by $f(x{\ast}y)+f(x{\ast}y^{-1})-2g(x)-2g(y)={\varphi}(x,y)$, $f(x{\ast}y)+g(x{\ast}y^{-1})-2h(x)-2k(y)={\varphi}(x,y)$, where (G, *) is a group, X is a real or complex Hausdorff topological vector space and f, g, h, k are functions from G into X.

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NOTES ON RANDOM FIXED POINT THEOREMS

  • Cho Y.J.;Khan M. Firdosh;Salahuddin Salahuddin
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제13권3호
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    • pp.227-236
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    • 2006
  • The purpose of this paper is to establish a random fixed point theorem for nonconvex valued random multivalued operators, which generalize known results in the literature. We also derive a random coincidence fixed point theorem in the noncompart setting.

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FIXED POINTS OF COUNTABLY CONDENSING MULTIMAPS HAVING CONVEX VALUES ON QUASI-CONVEX SETS

  • Hoonjoo Kim
    • 충청수학회지
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    • 제36권4호
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    • pp.279-288
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    • 2023
  • We obtain a Chandrabhan type fixed point theorem for a multimap having a non-compact domain and a weakly closed graph, and taking convex values only on a quasi-convex subset of Hausdorff locally convex topological vector space. We introduce the definition of Chandrabhan-set and find a sufficient condition for every countably condensing multimap to have a relatively compact Chandrabhan-set. Finally, we establish a new version of Sadovskii fixed point theorem for multimaps.

A selection theorem and its application

  • Lee, Gue-Myung;Kim, Do-Sang;Lee, Byung-Soo;Cho, Sung-Jin
    • 대한수학회논문집
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    • 제10권3호
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    • pp.759-766
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    • 1995
  • In this paper, we give equivalent forms of the selection theorem of Ding-Kim-Tan. As applications of the selection theorem of Ding-Kim-Tan, we obtain a fixed point theroem of Gale and Mas-Colell type and establish an equilibrium existence theorem for a qualitative game under suitable assumptions in a locally convex Hausdorff topological vector space.

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A NOTE ON THE HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC EQUATION

  • Kang, Jie-Hyung;Lee, Chang-Ju;Lee, Yang-Hi
    • 대한수학회보
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    • 제41권3호
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    • pp.541-557
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    • 2004
  • In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder ${\varphi}$ is defined by (x * y) + (x * $y^{-1}$) - 2 (x) - 2 (y) =<${\varphi}$(x,y), (x*y*z)+ (x)+ (y)+ (z)- (x*y)- (y*z)- (z*x)=${\varphi}$(x, y, z), where (G,*) is a group, X is a real or complex Hausdorff topological vector space, and is a function from G into X.