• Journal of applied mathematics & informatics
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• 제37권1_2호
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• pp.53-63
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• 2019

In this paper, we show the existence of solution of the neutral stochastic functional differential equations under non-Lipschitz condition, a weakened linear growth condition and a contractive condition. Furthermore, in order to obtain the existence of solution to the equation we used the Picard sequence.

• 대한수학회보
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• 제58권2호
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• pp.481-495
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• 2021

In this paper, we investigate the properties of Bergman spaces, Bloch spaces and integral means of p-harmonic functions on the unit ball in ℝn. Firstly, we offer some Lipschitz-type and double integral characterizations for Bergman space ��kγ. Secondly, we characterize Bloch space ��αω in terms of weighted Lipschitz conditions and BMO functions. Finally, a Hardy-Littlewood type theorem for integral means of p-harmonic functions is established.

• East Asian mathematical journal
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• 제25권4호
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• pp.425-431
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• 2009

We provide a local convergence analysis for Newton-like methods for the solution of generalized equations in a Banach space setting. Using some ideas of ours introduced in [2] for nonlinear equations we show that under weaker hypotheses and computational cost than in [7] a larger convergence radius and finer error bounds on the distances involved can be obtained.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.337-363
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• 2023

In this paper, we propose a new subgradient extragradient algorithm for finding a solution of monotone bilevel equilibrium problem in reflexive Banach spaces. The strong convergence of the algorithm is established under monotone assumptions of the cost bifunctions with Bregman Lipschitz-type continuous condition. Finally, a numerical experiments is reported to illustrate the efficiency of the proposed algorithm.

• 충청수학회지
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• 제37권1호
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• pp.41-55
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• 2024

The nonconvex and nonsmooth optimization problem has been widely applicable in image processing and machine learning. In this paper, we propose an extension of the proximal iteratively reweighted ℓ₁ algorithm for nonconvex and nonsmooth minmization problem. We assume the co-coerciveness of a term of objective function instead of Lipschitz gradient condition, which is generalized property of Lipschitz continuity. We prove the global convergence of the proposed algorithm. Numerical results show that the proposed algorithm converges faster than original proximal iteratively reweighed algorithm and existing algorithms.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.15-33
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• 2024

In this article, we considered a class of nonlinear variational hemivariational inequality problems and investigated a gap function and regularized gap function for the problems. We discussed the global error bounds for such inequalities in terms of gap function and regularized gap functions by utilizing the Clarke generalized gradient, relaxed monotonicity, and relaxed Lipschitz continuous mappings. Finally, as applications, we addressed an application to non-stationary non-smooth semi-permeability problems.

• 한국인터넷방송통신학회논문지
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• 제20권1호
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• pp.239-246
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• 2020

최근에 제안된 WGAN(Wasserstein generative adversarial network)의 등장으로 GAN(generative adversarial network)의 고질적인 문제인 까다롭고 불안정한 학습과정이 다소 개선되기는 하였으나 여전히 수렴이 안되거나 자연스럽지 못한 출력물을 생성하는 등의 경우가 발생한다. 이러한 문제를 해결하기 위하여 본 논문에서는 분별기가 실제 데이터 확률분포를 보다 정확히 추정할 수 있도록 표본화 과정을 개선하는 동시에 분별기 함수의 립쉬츠 연속조건을 안정적으로 유지시키기 위한 알고리즘을 제안한다. 다양한 실험을 통하여 제안 기법의 특성을 분석하고 성능을 확인한다.

• 대한전자공학회논문지SP
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• 제41권6호
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• pp.109-120
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• 2004

본 논문에서는 다층스케일 에지로부터 특이점 검출을 이용한 블록화 현상 제거 방법을 제안하였다. 블록 부호화된 영상에서 블록화 현상 및 에지와 같은 특이점들은 다층스케일 웨이블릿 변환 영역에서 국부 계수 최대치로 검출된다. 제안한 방법에서는 국부 계수 최대치의 Lipschitz 정칙 상수를 이용하여 블록화 현상 및 에지의 특이점들을 구분하고, 웨이블릿 변환 영역에서 블록화 현상에 의한 특이점들을 영역에 따라 스케일별로 제거한다. 실험 결과로부터 제안한 방법이 기존의 방법에 비하여 객관적 화질 및 주관적 화질 측면에서 보다 우수함을 확인하였다.

• 전기학회논문지
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• 제64권3호
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• pp.451-457
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• 2015

In this paper, we consider the observer design problem that truly reflects the nonlinear stiffness of the manipulators. The two key ideas of our design are that (a) estimation error dynamics of the manipulator equipped with accelerometer dose not dependent on nonlinearities at the link part, when the measured signals are the motor position and the output of the accelerometer and (b) the nonlinear stiffness is indeed a Lipschitz function. In order to effectively compensate the nonlinear stiffness, the gain of the proposed observer is carefully chosen from the ARE(algebraic Riccati equations) which depend on Lipschitz constant. Comparative simulation result verifies the effectiveness of the proposed solution.

• 대한수학회지
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• 제56권5호
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• pp.1333-1354
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• 2019

In authors' paper in 2007, it was shown that the BSE-extension of $C^1_0(R)$, the algebra of continuously differentiable functions f on the real number space R such that f and df /dx vanish at infinity, is the Lipschitz algebra $Lip_1(R)$. This paper extends this result to the case of $C^n_0(R^d)$ and $C^{n-1,1}_b(R^d)$, where n and d represent arbitrary natural numbers. Here $C^n_0(R^d)$ is the space of all n-times continuously differentiable functions f on $R^d$ whose k-times derivatives are vanishing at infinity for k = 0, ${\cdots}$, n, and $C^{n-1,1}_b(R^d)$ is the space of all (n - 1)-times continuously differentiable functions on $R^d$ whose k-times derivatives are bounded for k = 0, ${\cdots}$, n - 1, and (n - 1)-times derivatives are Lipschitz. As a byproduct of our investigation we obtain an important result that $C^{n-1,1}_b(R^d)$ has a predual.