• 대한수학회보
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• 제26권2호
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• pp.191-201
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• 1989

In this article we are interested in characterizing when metric projection is Lipschitz continuous and determining when metric selections which are also Lipschitz continuous exist.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.1182-1188
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• 2001

The objective of this paper is to show the effectiveness of the wavelet transform by means of its capability to estimate the Lipschitz exponent. In particular, we show that the magnitude of the Lipschitz exponent can be used as a useful tool estimating the damage extent. An effective method based on the Lipschitz exponent is proposed and we present the results investigated both numerically and experimentally. The continuous wavelet transform by a Mexican hat wavelet having two vanishing moments is utilized for the estimation of the Lipschitz exponent.

• Korean Journal of Mathematics
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• 제16권1호
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• pp.85-90
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• 2008

We consider Fourier multiplier operators whose symbols satisfy a generalization of $H{\ddot{o}}rmander^{\prime}s$ condition and establish their Sobolev-type mapping properties on the homogeneous Besov-Lipschitz spaces by making use of a continuous characterization of Besov-Lipschitz spaces. As an application, we derive Sobolev-type imbedding theorem.

• 충청수학회지
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• 제5권1호
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• pp.65-74
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• 1992

In this note, we show that the ${\omega}$-limit mapping is continuous and the Lipschitz constants vary continuously if the flow (x, ${\pi}$) is Lipschitz stable. Moreover we analyse the ${\omega}$-limit sets under the generalized locally Lipschitz stable flows.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.427-435
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• 2007

The existence theorem and continuous dependence property in $"L^2"$ sense for solutions of backward stochastic differential equation (shortly BSDE) with Lipschitz coefficients were respectively established by Pardoux-Peng and Peng in [1,2], Mao and Cao generalized the Pardoux-Peng's existence and uniqueness theorem to BSDE with non-Lipschitz coefficients in [3,4]. The present paper generalizes the Peng's continuous dependence property in $"L^2"$ sense to BSDE with Mao and Cao's conditions. Furthermore, this paper investigates the continuous dependence property in "almost surely" sense for BSDE with Mao and Cao's conditions, based on the comparison with the classical mathematical expectation.

• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.121-140
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• 2022

In this paper, we study the strong convergence of new methods for solving classical variational inequalities problems involving semistrictly quasimonotone and Lipschitz-continuous operators in a real Hilbert space. Three proposed methods are based on Tseng's extragradient method and use a simple self-adaptive step size rule that is independent of the Lipschitz constant. The step size rule is built around two techniques: the monotone and the non-monotone step size rule. We establish strong convergence theorems for the proposed methods that do not require any additional projections or knowledge of an involved operator's Lipschitz constant. Finally, we present some numerical experiments that demonstrate the efficiency and advantages of the proposed methods.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1179-1191
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• 2011

In this paper, we introduce a new iterative scheme for finding a common element of the set of fixed points of a finite family of strict pseudocontractions and the solution set of pseudomonotone and Lipschitz-type continuous equilibrium problems. The scheme is based on the idea of extragradient methods and fixed point iteration methods. We show that the iterative sequences generated by this algorithm converge strongly to the common element in a real Hilbert space.

• Korean Journal of Mathematics
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• 제25권1호
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• pp.19-35
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• 2017

In this communication, we introduce an Ishikawa type iterative algorithm for finding the approximate solutions of a class of nonlinear set valued variational inclusion problems. We also establish a characterization of strong convergence of this iterative techniques.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.313-321
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• 2004

In this paper we study the problem of three-dimensional layout optimization on the simplified rotating vessel of satellite. The layout optimization model with behavioral constraints is established and some effective and convenient conditions of performance optimization are presented. Moreover, we prove that the performance objective function is locally Lipschitz continuous and the results on the relations between the local optimal solution and the global optimal solution are derived.

• 대한수학회지
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• 제49권1호
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• pp.187-200
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• 2012

In this paper, we introduced a new extended extragradient iteration algorithm for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of equilibrium problems for a monotone and Lipschitz-type continuous mapping. And we show that the iterative sequences generated by this algorithm converge strongly to the common element in a real Hilbert space.