• Title, Summary, Keyword: Approximation-solvability

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APPROXIMATION-SOLVABILITY OF A CLASS OF A-MONOTONE VARIATIONAL INCLUSION PROBLEMS

  • Verma, Ram U.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.8 no.1
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    • pp.55-66
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    • 2004
  • First the notion of the A-monotonicity is applied to the approximation - solvability of a class of nonlinear variational inclusion problems, and then the convergence analysis is given based on a projection-like method. Results generalize nonlinear variational inclusions involving H-monotone mappings in the Hilbert space setting.

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THE SOLVABILITY CONDITIONS FOR A CLASS OF CONSTRAINED INVERSE EIGENVALUE PROBLEM OF ANTISYMMETRIC MATRICES

  • PAN XIAO-PING;HU XI-YAN;ZHANG LEI
    • Journal of the Korean Mathematical Society
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    • v.43 no.1
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    • pp.87-98
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    • 2006
  • In this paper, a class of constrained inverse eigenvalue problem for antisymmetric matrices and their optimal approximation problem are considered. Some sufficient and necessary conditions of the solvability for the inverse eigenvalue problem are given. A general representation of the solution is presented for a solvable case. Furthermore, an expression of the solution for the optimal approximation problem is given.

A NONCONFORMING PRIMAL MIXED FINITE ELEMENT METHOD FOR THE STOKES EQUATIONS

  • Cho, Sungmin;Park, Eun-Jae
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.6
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    • pp.1655-1668
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    • 2014
  • In this article, we propose and analyze a new nonconforming primal mixed finite element method for the stationary Stokes equations. The approximation is based on the pseudostress-velocity formulation. The incompressibility condition is used to eliminate the pressure variable in terms of trace-free pseudostress. The pressure is then computed from a simple post-processing technique. Unique solvability and optimal convergence are proved. Numerical examples are given to illustrate the performance of the method.

Approximation Solvability for a System of Nonlinear Variational Type Inclusions in Banach Spaces

  • Salahuddin, Salahuddin
    • Kyungpook Mathematical Journal
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    • v.59 no.1
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    • pp.101-123
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    • 2019
  • In this paper, we consider a system of nonlinear variational type inclusions involving ($H,{\varphi},{\eta}$)-monotone operators in real Banach spaces. Further, we define a proximal operator associated with an ($H,{\varphi},{\eta}$)-monotone operator and show that it is single valued and Lipschitz continuous. Using proximal point operator techniques, we prove the existence and uniqueness of a solution and suggest an iterative algorithm for the system of nonlinear variational type inclusions. Furthermore, we discuss the convergence of the iterative sequences generated by the algorithms.

ERROR ESTIMATION FOR NONLINEAR ELLIPTIC PROBLEMS USING THE h-p-MIXED FINITE ELEMENT METHOD IN 3 DIMENSIONAL SPACE

  • Lee, Mi-Young
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.2
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    • pp.237-260
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    • 2001
  • The approximation properties for $L^2$-projection, Raviart-Thomas projection, and inverse inequality have been derived in 3 dimensional space. h-p-mixed finite element methods for strongly nonlinear second order elliptic problems are proposed and analyzed in 3D. Solvability and convergence of the linearized problem have been shown through duality argument and fixed point argument. The analysis is carried out in detail using Raviart-Thomas-Nedelec spaces as an example.

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An improved linear sampled-data output regulators (개선된 선형 샘플치 출력 조절기)

  • 정선태
    • 제어로봇시스템학회:학술대회논문집
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    • pp.1726-1729
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    • 1997
  • In general, the solvability of linear robust output regulation problem are not preserved under time-sampling. Thus, it is found that the digital regulator implemented by itme-sampling of anlog output regulator designed based on the continuous-time linear system model is nothing but a 1st order approximation with respect to time-sampling. By the way, one can design an improved sampled-data regulator with respect to sampling time by utilizing the intrinsic structure of the system. In this paper, we study the system structures which it is possible to design an improved sampled-data regulator with respect to sampling time.

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ON NONLINEAR VARIATIONAL INCLUSIONS WITH ($A,{\eta}$)-MONOTONE MAPPINGS

  • Hao, Yan
    • East Asian mathematical journal
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    • v.25 no.2
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    • pp.159-169
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    • 2009
  • In this paper, we introduce a generalized system of nonlinear relaxed co-coercive variational inclusions involving (A, ${\eta}$)-monotone map-pings in the framework of Hilbert spaces. Based on the generalized resol-vent operator technique associated with (A, ${\eta}$)-monotonicity, we consider the approximation solvability of solutions to the generalized system. Since (A, ${\eta}$)-monotonicity generalizes A-monotonicity and H-monotonicity, The results presented this paper improve and extend the corresponding results announced by many others.

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A SYSTEM OF NONLINEAR VARIATIONAL INCLUSIONS WITH (A, $\eta$)-MONOTONE MAPPINGS IN HILBERT SPACES

  • Shang, Meijuan;Qin, Xiaolong
    • East Asian mathematical journal
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    • v.24 no.1
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    • pp.1-6
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    • 2008
  • In this paper, we introduce a system of nonlinear variational inclusions involving (A, $\eta$)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, $\eta$)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Our results improve and extend the recent ones announced by many others.

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GENERALIZED PROJECTION AND APPROXIMATION FOR GENERALIZED VARIATIONAL INEQUALITIES SYSTEM IN BANACH SPACES

  • He, Xin-Feng;Xu, Yong-Chun;He, Zhen
    • East Asian mathematical journal
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    • v.24 no.1
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    • pp.57-65
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    • 2008
  • The approximate solvability of a generalized system for non-linear variational inequality in Hilbert spaces was studied, based on the convergence of projection methods. But little research was done in Banach space. The primary reason was that projection mapping lacked preferably property in Banach space. In this paper, we introduced the generalized projection methods. By using these methods, the results presented in this paper extended the main results of S. S. Chang [3] from Hilbert spaces to Banach space.

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RELAXED PROXIMAL POINT ALGORITHMS BASED ON A-AXIMAL RELAXED MONOTONICITY FRAMEWORKS WITH APPLICATIONS

  • Agarwal, Ravi P.;Verma, Ram U.
    • East Asian mathematical journal
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    • v.27 no.5
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    • pp.545-555
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    • 2011
  • Based on the A-maximal(m)-relaxed monotonicity frameworks, the approximation solvability of a general class of variational inclusion problems using the relaxed proximal point algorithm is explored, while generalizing most of the investigations, especially of Xu (2002) on strong convergence of modified version of the relaxed proximal point algorithm, Eckstein and Bertsekas (1992) on weak convergence using the relaxed proximal point algorithm to the context of the Douglas-Rachford splitting method, and Rockafellar (1976) on weak as well as strong convergence results on proximal point algorithms in real Hilbert space settings. Furthermore, the main result has been applied to the context of the H-maximal monotonicity frameworks for solving a general class of variational inclusion problems. It seems the obtained results can be used to generalize the Yosida approximation that, in turn, can be applied to first- order evolution inclusions, and can also be applied to Douglas-Rachford splitting methods for finding the zero of the sum of two A-maximal (m)-relaxed monotone mappings.