• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권4호
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• pp.365-375
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• 2008

We present a new theorem for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. Under a gamma-type condition we show that we can extend the applicability of Newton's method given in [12]. We also provide a comparative study between results using the classical Newton-Kantorovich conditions ([6], [7], [10]), and the ones using the gamma-type conditions ([12], [13]). Numerical examples are also provided.

• 대한수학회지
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• 제48권4호
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• pp.727-747
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• 2011

By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.433-448
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• 1998

In this study we use inexact Newton-like methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a par-tially ordered Banach space. In this way the metric properties of the examined problem can be analyzed more precisely. Moreover this approach allows us to derive from the same theorem on the one hand semi-local results of kantorovich-type and on the other hand 2global results based on monotonicity considerations. By imposing very general Lipschitz-like conditions on the operators involved on the other hand by choosing our operators appropriately we can find sharper error bounds on the distances involved than before. Furthermore we show that special cases of our results reduce to the corresponding ones already in the literature. Finally our results are used to solve integral equations that cannot be solved with existing methods.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.139-159
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• 2000

In this manuscript we study perturbed Newton-like methods for the solution of nonlinear operator equations in a Banach space and their discretized versions in connection with the mesh independence principle. This principle asserts that the behavior of the discretized process is asymptotically the same as that for the original iteration and consequently, the number of steps required by the two processes to converge to within a given tolerance is essentially the same. So far this result has been proved by others using Newton's method for certain classes of boundary value problems and even more generally by considering a Lipschitz uniform discretization. In some of our earlierpapers we extend these results to include Newton-like methods under more general conditions. However, all previous results assume that the iterates can be computed exactly. This is mot true in general. That in why we use perturbed Newton-like methods and even more general conditions. Our results, on the one hand, extend, and on the other hand, make more practical and applicable all previous results.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2001년도 추계학술대회 학술발표 논문집
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• pp.337-340
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• 2001

In this paper, we consider the observability conditions for the following nonlinear fuzzy neutral functional differential equations : (equation omitted), where x(t) is state function on E$\_$N/$\^$2/, u(t) is control function on E$\_$N/$\^$2/ and nonlinear continuous functions f:J C$\_$0/ E$\_$N/$\^$2/, k:J C$\_$0/ E$\_$N/$\^$2/ are satisfies global Lipschitz conditions.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.1604-1607
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• 2004

In this paper, we consider a problem of asymptotic output regulation of a class of uncertain nonlinear systems by output feedback. The system under consideration is in the Parametric-Pure-Feedback Form, which does not satisfy the existing conditions such as the triangularity condition or the Lipschitz condition. We propose a linear output feedback controller with a scaling factor, which asymptotically regulates the output of the considered system.

• 대한수학회논문집
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• 제19권1호
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• pp.63-74
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• 2004

Suppose that X is a real Banach space, K is a nonempty closed convex subset of X and T : $K\;\rightarrow\;K$ is a uniformly continuous ${\phi}$-hemicontractive operator or a Lipschitz ${\phi}-hemicontractive$ operator. In this paper we prove that under certain conditions the three-step iteration methods with errors converge strongly to the unique fixed point of T. Our results extend the corresponding results of Chang [1], Chang et a1. [2], Chidume [3]-[7], Chidume and Osilike [9], Deng [10], Liu and Kang [13], [14], Osilike [15], [16] and Tan and Xu [17].

• 대한수학회보
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• 제51권1호
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• pp.221-227
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• 2014

Our goal is to relax a sufficient condition for the exponential almost sure stability of a certain class of stochastic differential equations. Compared to the existing theory, we prove the almost sure stability, replacing Lipschitz continuity and linear growth conditions by the existence of a strong solution of the underlying stochastic differential equation. This result is extendable for the regime-switching system. An explicit example is provided for the illustration purpose.

• 대한수학회보
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• 제51권1호
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• pp.287-301
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• 2014

In this paper, we prove a necessary optimality theorem for a nonsmooth optimization problem in the face of data uncertainty, which is called a robust optimization problem. Recently, the robust optimization problems have been intensively studied by many authors. Moreover, we give examples showing that the convexity of the uncertain sets and the concavity of the constraint functions are essential in the optimality theorem. We present an example illustrating that our main assumptions in the optimality theorem can be weakened.

• 대한수학회보
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• 제41권2호
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• pp.241-256
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• 2004

In this paper, we introduce and study a new class of variational inclusions, called the general variational inclusion. We prove the equivalence between the general variational inclusions, the general resolvent equations, and the fixed-point problems, using the resolvent operator technique. This equivalence is used to suggest and analyze a few iterative algorithms for solving the general variational inclusions and the general resolvent equations. Under certain conditions, the convergence analyses are also studied. The results presented in this paper generalize, improve and unify a number of recent results.