• 제목/요약/키워드: convex space

검색결과 408건 처리시간 0.026초

FIXED POINTS OF BETTER ADMISSIBLE MAPS ON GENERALIZED CONVEX SPACES

  • Park, Se-Hie
    • 대한수학회지
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    • 제37권6호
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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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FIXED POINT THEOREMS ON GENERALIZED CONVEX SPACES

  • Kim, Hoon-Joo
    • 대한수학회지
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    • 제35권2호
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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
    • 대한수학회지
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    • 제39권3호
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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.

THE PROXIMAL POINT ALGORITHM IN UNIFORMLY CONVEX METRIC SPACES

  • Choi, Byoung Jin;Ji, Un Cig
    • 대한수학회논문집
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    • 제31권4호
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    • pp.845-855
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    • 2016
  • We introduce the proximal point algorithm in a p-uniformly convex metric space. We first introduce the notion of p-resolvent map in a p-uniformly convex metric space as a generalization of the Moreau-Yosida resolvent in a CAT(0)-space, and then we secondly prove the convergence of the proximal point algorithm by the p-resolvent map in a p-uniformly convex metric space.

GEOMETRY OF CONTACT STRONGLY PSEUDO-CONVEX CR-MANIFOLDS

  • Cho, Jong-Taek
    • 대한수학회지
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    • 제43권5호
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    • pp.1019-1045
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    • 2006
  • As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,\;\eta,\;\varphi)$ with the pseudo-parallel structure operator $h(=1/2L\xi\varphi)$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $L\xi$ denote the Lie derivative in the characteristic direction $\xi$.

퍼지 수 공간의 컴팩트 볼륵 집합에 관한 연구 (On compact convex subsets of fuzzy number space)

  • Kim, Yun-Kyong
    • 한국지능시스템학회:학술대회논문집
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    • 한국퍼지및지능시스템학회 2003년도 춘계 학술대회 학술발표 논문집
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    • pp.14-17
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    • 2003
  • By Mazur's theorem, the convex hull of a relatively compact subset a Banach space is also relatively compact. But this is not true any more in the space of fuzzy numbers endowed with the Hausdorff-Skorohod metric. In this paper, we establish a necessary and sufficient condition for which the convex hull of K is also relatively compact when K is a relatively compact subset of the space F(R$\^$k/) of fuzzy numbers of R$\^$k/ endowed with the Hausdorff-Skorohod metric.

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A METHOD FOR TESTING SURFACE DEFORMS OF LARGE CONVEX MIRRORS

  • Kim Young-Soo
    • 한국우주과학회:학술대회논문집(한국우주과학회보)
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    • 한국우주과학회 2004년도 한국우주과학회보 제13권2호
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    • pp.254-257
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    • 2004
  • Both ground and space telescopes are being built larger and larger. Accordingly, the secondary mirrors become larger which are convex mostly on the surface form. Testing convex mirrors becomes more difficult and delicate than testing concave mirrors in optics, because additional optical components are needed to make the reflected rays converge. Hindle type tests are frequently used for measuring the surface deforms of convex mirrors, which employs a meniscus lens to reverse the diverted rays from the mirrors. In case of testing large convex mirrors by using Hindle type tests, attention would be needed as larger meniscus lens is required. A method of modified Hindle test has been studied and the characteristics are analyzed. In this paper, current method of testing convex mirrors is presented, and a new method is discussed.

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A PROOF OF A CONVEX-VALUED SELECTION THEOREM WITH THE CODOMAIN OF A FRECHET SPACE

  • Cho, Myung-Hyun;Kim, Jun-Hui
    • 대한수학회논문집
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    • 제16권2호
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    • pp.277-285
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    • 2001
  • The purpose of this paper is to give a proof of a generalized convex-valued selection theorem which is given by weakening a Banach space to a completely metrizable locally convex topological vector space, i.e., a Frechet space. We also develop the properties of upper semi-continuous singlevalued mapping to those of upper semi-continuous multivalued mappings. These properties wil be applied in our further consideraations of selection theorems.

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