• Journal of the Korean Statistical Society
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• v.26 no.2
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• pp.231-243
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• 1997

In this paper we investigate weak convergence of the intergral processes whose index set is the non-compact infinite time interval. Our first goal is to develop the empirical central limit theorem as random elements of [0, .infty.) for an integral process which is constructed from iid variables. In developing the weak convergence as random elements of D[0, .infty.), we will use a result of Ossiander(4) whose proof heavily depends on the total boundedness of the index set. Our next goal is to establish the empirical central limit theorem for the Kaplan-Meier integral process as random elements of D[0, .infty.). In achieving the the goal, we will use the above iid result, a representation of State(6) on the Kaplan-Meier integral, and a lemma on the uniform order of convergence. The first result, in some sense, generalizes the result of empirical central limit therem of Pollard(5) where the process is regarded as random elements of D[-.infty., .infty.] and the sample paths of limiting Gaussian process may jump. The second result generalizes the first result to random censorship model. The later also generalizes one dimensional central limit theorem of Stute(6) to a process version. These results may be used in the nonparametric statistical inference.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.781-793
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• 2016

The solutions of equations are usually found using iterative methods whose convergence order is determined by Taylor expansions. In particular, the local convergence of the method we study in this paper is shown under hypotheses reaching the third derivative of the operator involved. These hypotheses limit the applicability of the method. In our study we show convergence of the method using only the first derivative. This way we expand the applicability of the method. Numerical examples show the applicability of our results in cases earlier results cannot.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.1-17
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• 2004

The famous Newton-Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton method to a solution of an equation in connection with the Lipschitz continuity of the Frechet-derivative of the operator involved. Using Lipschitz and center-Lipschitz conditions we show that the Newton-Kantorovich hypothesis is weakened. The error bounds obtained under our semilocal convergence result are finer and the information on the location of the solution more precise than the corresponding ones given by the dominating Newton-Kantorovich theorem, and under the same hypotheses/computational cost, since the evaluation of the Lipschitz also requires the evaluation of the center-Lipschitz constant. In the case of local convergence we obtain a larger convergence radius than before. This observation is important in computational mathematics and can be used in connection to projection methods and in the construction of optimum mesh independence refinement strategies.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.543-549
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• 2006

Sung et al. [13] obtained a WLLN (weak law of large numbers) for the array $\{X_{{ni},\;u_n{\leq}i{\leq}v_n,\;n{\leq}1\}$ of random variables under a Cesaro type condition, where $\{u_n{\geq}-{\infty},\;n{\geq}1\}$ and $\{v_n{\leq}+{\infty},\;n{\geq}1\}$ large two sequences of integers. In this paper, we extend the result of Sung et al. [13] to a martingale type p Banach space.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.273-285
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• 1999

In this paper we establish the weak law of large numbers for randomly weighted partial sums of random variables and study conditions imposed on the triangular array of random weights {$W_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}n{\geq}1$} and on the triangular array of random variables {$X_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}{\geq}1$} which ensure that $\sum_{j=1}^{n}{\;}W_{nj}{\mid}X_{nj}{\;}-{\;}B_{nj}{\mid}$ converges In probability to 0, where {$B_{nj}{\;}:{\;}1{\;}{\leq}{\;}j{\;}{\leq}{\;}n,{\;}n{\;}{\geq}{\;}1$} is a centering array of constants or random variables.

• Journal of Korea Multimedia Society
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• v.23 no.12
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• pp.1507-1518
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• 2020

Recently, as the proportion of the elderly population in Korea has increased rapidly, it has entered an aging society. As the scope of social activities of the elderly increases, the risk of safety accidents is also increasing. The traffic accident rate of elderly pedestrians is higher than ordinary people. Although various smart devices for the elderly are researched and developed, electronic components are often used. Electronic devices may not be able to be used if charging is not regularly. In this paper, a smart hat, a smart system for the elderly and the weak, was implemented using solar panels. The system uses solar energy to provide reliable use of smart devices. It is believed to be helpful not only for the elderly but also for the weak people by easy to wear the hat.

• Journal of Digital Convergence
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• v.12 no.5
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• pp.69-78
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• 2014

This study deals with the digital policy proposal through the path modeling study on the effect of the strength of weak ties & emotional perception leading to the user's satisfaction, WOM between game users, and the verification on the effect of the emotional real name SNS on the social network game's diffusion. Researcher confirmed that the effect of the strength of weak ties & emotional perception led to the user's satisfaction, WOM of SNG. Even though weak tie, researchers estimate that the users emotionally interact with the real name relation effect of SNS. And effective factors for WOM are not a tie relationship or emotional interactivity of weak tie antecedently but user's satisfaction. As a result, though antecedent factors (weak tie & interactivity) had a positive effect as real name SNS, eventually powerful factor of making buzz was the SNG user's satisfaction. Thus researchers expect the practical policy proposition for government & corporation, which means SNG service providers more carefully manage the service satisfaction for WOM with SNG user's experience.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.955-970
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• 2014

We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than in earlier studies such us [10, 11, 13, 14, 18]. Special cases and numerical examples are also included in this study.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.763-771
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• 2009

T.H. Kim, H.K. Xu, [Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal.(2007),doi:l0.l016/j.na.2007.02.029.] proved the strong convergence for asymptotically strict pseudo-contractions by the classical CQ iterative method. In this paper, we apply the monotone CQ iterative method to modify the classical CQ iterative method of T.H. Kim, H.K. Xu, and to obtain the strong convergence theorems for asymptotically strict pseudo-contractions. In the proved process of this paper, Cauchy sequences method is used, so we complete the proof without using the demi-closedness principle, Opial's condition or others about weak topological technologies. In addition, we use a ingenious technology to avoid defining that F(T) is bounded. On the other hand, we relax the restriction on the control sequence of iterative scheme.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.757-777
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• 2019

In this paper, we study the convergence analysis of the sequences generated by the proximal point method for an infinite family of pseudo-monotone equilibrium problems in Banach spaces. We first prove the weak convergence of the generated sequence to a common solution of the infinite family of equilibrium problems with summable errors. Then, we show the strong convergence of the generated sequence to a common equilibrium point by some various additional assumptions. We also consider two variants for which we establish the strong convergence without any additional assumption. For both of them, each iteration consists of a proximal step followed by a computationally inexpensive step which ensures the strong convergence of the generated sequence. Also, for this two variants we are able to characterize the strong limit of the sequence: for the first variant it is the solution lying closest to an arbitrarily selected point, and for the second one it is the solution of the problem which lies closest to the initial iterate. Finally, we give a concrete example where the main results can be applied.