• Journal of applied mathematics & informatics
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• v.37 no.1_2
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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.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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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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• v.25 no.4
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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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• v.28 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.1
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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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• v.29 no.1
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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.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.20 no.1
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• pp.239-246
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• 2020

The recently proposed Wasserstein generative adversarial network (WGAN) has improved some of the tricky and unstable training processes that are chronic problems of the generative adversarial network(GAN), but there are still cases where it generates poor samples or fails to converge. In order to solve the problems, this paper proposes algorithms to improve the sampling process so that the discriminator can more accurately estimate the data probability distribution to be modeled and to stably maintain the discriminator should be Lipschitz continuous. Through various experiments, we analyze the characteristics of the proposed techniques and verify their performances.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.6
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• pp.109-120
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• 2004

The current paper presents an effective deblocking algorithm for block-based coded images using singularity detection in Mallat wavelet transform. In block-based coded images. The local maxima of the wavelet transform modulus detect all singularities, including blocking artifacts, from multiscale edges. Accordingly, the current study discriminates between blocking artifacts and edges by estimating the Lipschitz regularity of the local maxima and removing the wavelet transform modulus of blocking artifacts. Experimental results showed that the performance of the proposed algorithm was objectively and subjectively superior.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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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.