• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권2호
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• pp.55-64
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• 2005

In this paper, generalized difference methods(GDM) for one-dimensional viscoelastic problems are proposed and analyzed. The new initial values are given in the generalized difference scheme, so we obtain optimal error estimates in $L^p$ and $W^{1,p}(2\;{\leq}\;p\;{\leq}\;{\infty})$ as well as some superconvergence estimates in $W^{1,p}(2\;{\leq}\;p\;{\leq}\;{\infty})$ between the GDM solution and the generalized Ritz-Volterra projection of the exact solution.

• 한국자동차공학회논문집
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• 제5권1호
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• pp.154-161
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• 1997

This paper presents the method to eliminate the constraint reaction in the Lagrange multiplier form equation of motion by using a generalized coordinate driveder from the velocity constraint equation. This method introduces a matrix method by considering the m dimensional space spanned by the rows of the constraint jacobian matrix. The orthogonal vectors defining the constraint manifold are projected to null vectors by the tangential vectors defined on the constraint manifold. Therefore the orthogonal projection matrix is defined by the tangential vectors. For correcting the generalized position coordinate, the optimization problem is formulated. And this correction process is analyzed by the quasi Newton method. Finally this method is verified through 3 dimensional vehicle model.

• East Asian mathematical journal
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• 제30권1호
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• pp.69-77
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• 2014

In this paper, we introduce a new generalized resolvent in a Banach space and discuss its some properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping. Furthermore, strong convergence of the scheme to a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping is proved.

• Korean Journal of Mathematics
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• 제24권2호
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• pp.181-198
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• 2016

In this work, we suggest a new system of generalized nonlinear regularized nonconvex variational inequalities in a real Hilbert space and establish an equivalence relation between this system and fixed point problems. By using the equivalence relation we suggest a new perturbed projection iterative algorithms with mixed errors for finding a solution set of system of generalized nonlinear regularized nonconvex variational inequalities.

• 충청수학회지
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• 제23권4호
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• pp.801-812
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• 2010

In this paper, we consider the convergence of the shrinking projection method for quasi-$\phi$-nonexpansive mappings. Strong convergence theorems are established in a uniformly smooth and strictly convex Banach space which enjoys the Kadec-Klee property.

• 한국인구학
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• 제12권2호
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• pp.56-68
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• 1989

The methodology in historical demography comprises the three core areas the family reconstitution method at the Institut National d' Ftudes Demographiques(I.N.E.D), the back projection at the Cambridge Group for the History of PopuJation and Social Struc-ture(HPSS). and the household-pattern analysis at the Cambridge Group and at the California Institute of Technology. The paper presents an outline of the family reconstitu-tion method and discusses the problems, both theoretical and methodological, arising from the problematic back projection vis-a-vis the usual inverse projection developed by Ronald D. Lee at Berkeley. Recent developments in the tield of the generalized inverse projection method designed 10 supplement the defects in the back projection and the inverse projection are presented. and for ease of explanation of the parish register data for the family reconstitution form (FRE). pre-modern Korean household register data are presented along with the parish register data of England and Wales that constitute the backbone of historical demography in pre-modern Europe. Possibilities of exploring the household pattern analysis method based on the Laslett-Hammel classification scheme for the mid-eighteenth-century Korean household register data are suggested.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.465-472
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• 2010

The purpose of this article is to introduce a new generalized class of the Wiener-Hopf equations and a new generalized class of the variational inequalities. Using the projection technique, we show that the generalized Wiener-Hopf equations are equivalent to the generalized variational inequalities. We use this alternative equivalence to suggest and analyze an iterative scheme for finding the solution of the generalized Wiener-Hopf equations and the solution of the generalized variational inequalities. The results presented in this paper may be viewed as significant and improvement of the previously known results. In special, our results improve and extend the resent results of M.A. Noor and Z.Y.Huang[M.A. Noor and Z.Y.Huang, Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings, Appl. Math. Comput.(2007), doi:10.1016/j.amc.2007.02.117].

• 대한수학회지
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• 제52권6호
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• pp.1179-1194
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• 2015

In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.

• East Asian mathematical journal
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• 제29권3호
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• pp.303-314
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• 2013

In this paper, we introduce an iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem and the set of common fixed points of a finite family of asymptotically ${\kappa}$-strict pseudo-contractions in Hilbert spaces. Weak and strong convergence theorems are established for the iterative scheme.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1263-1275
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• 2010

In this paper, we introduce a new iterative scheme for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings and the set of solutions to a generalized equilibrium problem and the set of solutions to a variational inequality problem in a real Hilbert space. Then strong convergence of the scheme to a common element of the three sets is proved. As applications, three new strong convergence theorems are obtained. Our theorems extend important recent results.