• 제목/요약/키워드: k smooth spaces

검색결과 104건 처리시간 0.028초

GENERAL NONLINEAR RANDOM SET-VALUED VARIATIONAL INCLUSION PROBLEMS WITH RANDOM FUZZY MAPPINGS IN BANACH SPACES

  • Balooee, Javad
    • 대한수학회논문집
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    • 제28권2호
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    • pp.243-267
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    • 2013
  • This paper is dedicated to study a new class of general nonlinear random A-maximal $m$-relaxed ${\eta}$-accretive (so called (A, ${\eta}$)-accretive [49]) equations with random relaxed cocoercive mappings and random fuzzy mappings in $q$-uniformly smooth Banach spaces. By utilizing the resolvent operator technique for A-maximal $m$-relaxed ${\eta}$-accretive mappings due to Lan et al. and Chang's lemma [13], some new iterative algorithms with mixed errors for finding the approximate solutions of the aforesaid class of nonlinear random equations are constructed. The convergence analysis of the proposed iterative algorithms under some suitable conditions are also studied.

DECOMPOSITION OF CONTINUITY AND COMPLETE CONTINUITY IN SMOOTH FUZZY TOPOLOGICAL SPACES

  • Amudhambigai, B.;Uma, M.K.;Roja, E.
    • East Asian mathematical journal
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    • 제27권3호
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    • pp.261-271
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    • 2011
  • In this paper, fuzzy ${\alpha}^*$-set, fuzzy C-set, fuzzy AB-set, fuzzy t-set, fuzzy B-set, etc., are introduced in the sense of Sostak [12] and Ramadan [9]. By using these sets, a decomposition of fuzzy continuity and complete fuzzy continuity are provided. Characterization of smooth fuzzy extremally disconnected spaces is also obtained in this connection.

A SYSTEM OF NONLINEAR VARIATIONAL INCLUSIONS IN REAL BANACH SPACES

  • Bai, Chuan-Zhi;Fang, Jin-Xuan
    • 대한수학회보
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    • 제40권3호
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    • pp.385-397
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    • 2003
  • In this paper, we introduce and study a system of nonlinear implicit variational inclusions (SNIVI) in real Banach spaces: determine elements $x^{*},\;y^{*},\;z^{*}\;\in\;E$ such that ${\theta}\;{\in}\;{\alpha}T(y^{*})\;+\;g(x^{*})\;-\;g(y^{*})\;+\;A(g(x^{*}))\;\;\;for\;{\alpha}\;>\;0,\;{\theta}\;{\in}\;{\beta}T(z^{*})\;+\;g(y^{*})\;-\;g(z^{*})\;+\;A(g(y^{*}))\;\;\;for\;{\beta}\;>\;0,\;{\theta}\;{\in}\;{\gamma}T(x^{*})\;+\;g(z^{*})\;-\;g(x^{*})\;+\;A(g(z^{*}))\;\;\;for\;{\gamma}\;>\;0,$ where T, g : $E\;{\rightarrow}\;E,\;{\theta}$ is zero element in Banach space E, and A : $E\;{\rightarrow}\;{2^E}$ be m-accretive mapping. By using resolvent operator technique for n-secretive mapping in real Banach spaces, we construct some new iterative algorithms for solving this system of nonlinear implicit variational inclusions. The convergence of iterative algorithms be proved in q-uniformly smooth Banach spaces and in real Banach spaces, respectively.

FRACTIONAL ORDER SOBOLEV SPACES FOR THE NEUMANN LAPLACIAN AND THE VECTOR LAPLACIAN

  • Kim, Seungil
    • 대한수학회지
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    • 제57권3호
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    • pp.721-745
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    • 2020
  • In this paper we study fractional Sobolev spaces characterized by a norm based on eigenfunction expansions. The goal of this paper is twofold. The first one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 2 equipped with a norm defined in terms of Neumann eigenfunction expansions. Due to the zero Neumann trace of Neumann eigenfunctions on a boundary, fractional Sobolev spaces of order 3/2 ≤ s ≤ 2 characterized by the norm are the spaces of functions with zero Neumann trace on a boundary. The spaces equipped with the norm are useful for studying cross-sectional traces of solutions to the Helmholtz equation in waveguides with a homogeneous Neumann boundary condition. The second one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 1 for vector-valued functions in a simply-connected, bounded and smooth domain in ℝ2. These spaces are defined by a norm based on series expansions in terms of eigenfunctions of the vector Laplacian with boundary conditions of zero tangential component or zero normal component. The spaces defined by the norm are important for analyzing cross-sectional traces of time-harmonic electromagnetic fields in perfectly conducting waveguides.

FUZZY R-CLUSTER AND FUZZY R-LIMIT POINTS

  • Kim, Yong Chan;Kim, Young Sun
    • Korean Journal of Mathematics
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    • 제8권1호
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    • pp.63-72
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    • 2000
  • In this paper, we introduce the notions of fuzzy r-cluster and fuzzy r-limit points in smooth fuzzy topological spaces and investigate some of their properties.

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Fuzzy r-convergent nets

  • Kim, Yong-Chan;Kim, Young-Sun
    • 한국지능시스템학회논문지
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    • 제10권5호
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    • pp.513-519
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    • 2000
  • In this paper, we investigate some properties of fuzzy r-cluster points and fuzzy r-limit points in smooth fuzzy topological spaces. We define fuzzy r-convergent nets and investigate some of their properties.

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A SYSTEM OF NONLINEAR SET-VALUED IMPLICIT VARIATIONAL INCLUSIONS IN REAL BANACH SPACES

  • Bai, Chuanzhi;Yang, Qing
    • 대한수학회논문집
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    • 제25권1호
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    • pp.129-137
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    • 2010
  • In this paper, we introduce and study a system of nonlinear set-valued implicit variational inclusions (SNSIVI) with relaxed cocoercive mappings in real Banach spaces. By using resolvent operator technique for M-accretive mapping, we construct a new class of iterative algorithms for solving this class of system of set-valued implicit variational inclusions. The convergence of iterative algorithms is proved in q-uniformly smooth Banach spaces. Our results generalize and improve the corresponding results of recent works.