• 대한수학회지
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• 제32권3호
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• pp.493-507
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• 1995

The Hartman-Stampacchia variational inequality was first suggested and studied by Hartman and Stampacchia [8] in finite dimensional spaces during the time establishing the base of variational inequality theory in 1960s [4]. Then it was generalized by Lions et al. [6], [9], [10], Browder [3] and others to the case of infinite dimensional inequality [3], [9], [10], and the results concerning this variational inequality have been applied to many important problems, i.e., mechanics, control theory, game theory, differential equations, optimizations, mathematical economics [1], [2], [6], [9], [10]. Recently, the Browder-Hartman-Stampaccnia variational inequality was extended to the case of set-valued monotone mappings in reflexive Banach sapces by Shih-Tan [11] and Chang [5], and under different conditions, they proved some existence theorems of solutions of this variational inequality.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2000년도 추계학술대회 학술발표 논문집
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• pp.168-171
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• 2000

This paper is concerned with fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in E$\_$N/ We study continuously initial observability for the following fuzzy system. x(t)=a(t)x(t)+f(t,x(t)), x(0)=x$\_$0/, y(t)=$\_$${\alpha}$/∏(x(t)), where a: [0, T]\longrightarrowE$\_$N/ is fuzzy coefficient, initial value x$\_$0/$\in$E$\_$N/ and nonlinear funtion f: [0, T]${\times}$E$\_$N/\longrightarrowE$\_$N/ satisfies a Lipschitz condition. Given fuzzy mapping ∏: C([0, T]: E$\_$N/)\longrightarrowY and Y is an another E$\_$N/.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.13-23
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• 2009

Some strong convergence theorems of explicit iteration scheme for asymptotically nonexpansive semi-groups in Banach spaces are established. The results presented in this paper extend and improve some recent results in [T. Suzuki. On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131(2002)2133-2136; H. K. Xu. A strong convergence theorem for contraction semigroups in Banach spaces, Bull. Aust. Math. Soc. 72(2005)371-379; N. Shioji and W. Takahashi. Strong convergence theorems for continuous semigroups in Banach spaces, Math. Japonica. 1(1999)57-66; T. Shimizu and W. Takahashi. Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl. 211(1997)71-83; N. Shioji and W. Takahashi. Strong convergence theorems for asymptotically nonexpansive mappings in Hilbert spaces, Nonlinear Anal. TMA, 34(1998)87-99; H. K. Xu. Approximations to fixed points of contraction semigroups in Hilbert space, Numer. Funct. Anal. Optim. 19(1998), 157-163.]

• Journal of applied mathematics & informatics
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• 제35권5_6호
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• pp.423-438
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• 2017

The aim of this paper is to present two new viscosity rules for nonexpansive mappings in Hilbert spaces. Under some assumptions, the strong convergence theorems of the purposed new viscosity rules are proved. Some applications are also included.

• 전기학회논문지
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• 제62권8호
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• pp.1120-1124
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• 2013

Our objective of this study was to reduce radio frequency coil (RF) control time at 3 T MRI systems. A compressed method is proposed with a convex optimization and pseudo-inverse method in multi-channel RF coils. After applying the proposed methods, fields are homogenized with less field data. Even with 80% compression, the fields are well homogenized and localized, indicating that mapping requires only 20% of the original data. Detailed values are compared between each compressed result in and outside the region of interest at 3 T.

• 대한수학회보
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• 제34권2호
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• pp.273-285
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• 1997

The aim of this paper is to present theorems on the exitence of zeros for mappings defined on convex subsets of topological vector spaces with values in a vector space. In addition to natural assumptions of continuity, convexity, and compactness, the mappings are subject to some geometric conditions. In the first theorem, the mapping satisfies a "Darboux-type" property expressed in terms of an auxiliary numerical function. Typically, this functions is, in this case, related to an order structure on the target space. We derive an existence theorem for "obtuse" quasiconvex mappings with values in an ordered vector space. In the second theorem, we prove the existence of a "common zero" for an arbitrary (not necessarily countable) family of mappings satisfying a general "inwardness" condition againg expressed in terms of numerical functions (these numerical functions could be duality pairings (more generally, bilinear forms)). Our inwardness condition encompasses classical inwardness conditions of Leray-Schauder, Altman, or Bergman-Halpern types.

• 대한수학회보
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• 제36권1호
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• pp.147-159
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• 1999

Tabanov investigated the global symmetric perturbation of the integrable billiard mapping in the ellipse [3]. He showed the nonintegrability of the Birkhoff billiard in the perturbed domain by proving that the principal separatrices splitting angle is not zero.In this paper, using the exact separatrix map of an one-degree-of freedom Hamiltoniam system with time periodic perturbation, we show the existence the stochastic layer including the uniformly hyperbolic invariant set which implies the nonintegrability near the separatrices of a Birkhoff's billiard in the domain bounded by $C^2$ convex simple curve constructed by the generic global perturbation of the ellipse.

• 한국정보통신학회논문지
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• 제6권4호
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• pp.645-651
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• 2002

본 논문에서는 전체적으로 묘사된 얼굴의 특징을 이용하여 얼굴 영상을 합성하는 방법을 제안한다. 제안된 방법은 얼굴의 형태를 대조하는 방법을 이용하여 만든 원영상의 작은 부분 영상들을 가지고 얼굴을 재현하였으며 얼굴 영상에서 2차원적 형태와 구조를 분리함으로서 음영부분과 경계부분을 표현할 수 있었으며, 영상과 영상의 특성을 나타내는 얼굴 부분영역을 조화롭게 재배치함으로서 합성을 가능케 하였다. 실험결과 본 논문에서 제안된 방법으로 합성한 얼굴 영상은 항상 자연스러운 얼굴 영상을 나타냄으로서 제안된 방법의 실효성을 입증하였다.

• 대한수학회논문집
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• 제11권3호
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• pp.725-742
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• 1996

In this paper we give some sharp expressions of the weakly convergent sequence coefficient WCS(X) of a Banach space X. They are used to prove fixed point theorems for involution mappings T from a weakly compact convex subset C of a Banach space X with WCS(X) > 1 into itself which $T^2$ are both of asymptotically nonexpansive type and weakly asymptotically regular on C. We also show that if X satisfies the semi-Opial property, then every nonexpansive mapping $T : C \to C$ has a fixed point. Further, some questions for asymtotically nonexpansive mappings are raised.

• East Asian mathematical journal
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• 제24권3호
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• pp.305-315
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• 2008

The purpose of this paper is to study the existence and uniqueness of the fixed point of uniformly pseudo-contractive operator and the solution of equation with uniformly accretive operator, and to approximate the fixed point and the solution by the Mann iterative sequence in an arbitrary Banach space or an uniformly smooth Banach space respectively. The results presented in this paper show that if X is a real Banach space and A : X $\rightarrow$ X is an uniformly accretive operator and (I-A)X is bounded then A is a mapping onto X when A is continuous or $X^*$ is uniformly convex and A is demicontinuous. Consequently, the corresponding results which depend on the assumptions that the fixed point of operator and solution of the equation are in existence are improved.