• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.823-834
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• 2007

We introduce a new system of generalized nonlinear mixed quasivariational inequalities and prove the existence and uniqueness of the solution for the system in Hilbert spaces. The main result of this paper is an extension and improvement of the well-known corresponding results in Kim-Kim [16], Noor [21]-[23] and Verma [24]-[26].

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.661-670
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• 2005

In this paper, we deal with approximations of com­mon fixed points of the iterative sequences with errors for three asymptotically nonexpansive mappings in a uniformly convex Banach space. Our results generalize and improve the corresponding results of Khan and Takahashi, Schu, Takahashi and Tamura, and others.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1061-1073
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• 1999

Let X be a real normed linear space. Let T : D(T) ⊂ X \longrightarrow X be a uniformly continuous and ∮-strongly quasi-accretive mapping. Let {${\alpha}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} , {${\beta}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} be two real sequences in [0, 1] satisfying the following conditions: (ⅰ) ${\alpha}$n \longrightarrow0, ${\beta}$n \longrightarrow0, as n \longrightarrow$\infty$ (ⅱ) {{{{ SUM from { { n}=0} to inf }}}} ${\alpha}$=$\infty$. Set Sx=x-Tx for all x $\in$D(T). Assume that {u}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} and {v}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} are two sequences in D(T) satisfying {{{{ SUM from { { n}=0} to inf }}}}∥un∥<$\infty$ and vn\longrightarrow0 as n\longrightarrow$\infty$. Suppose that, for any given x0$\in$X, the Ishikawa type iteration sequence {xn}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} with errors defined by (IS)1 xn+1=(1-${\alpha}$n)xn+${\alpha}$nSyn+un, yn=(1-${\beta}$n)x+${\beta}$nSxn+vn for all n=0, 1, 2 … is well-defined. we prove that {xn}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} converges strongly to the unique zero of T if and only if {Syn}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} is bounded. Several related results deal with iterative approximations of fixed points of ∮-hemicontractions by the ishikawa iteration with errors in a normed linear space. Certain conditions on the iterative parameters {${\alpha}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} , {${\beta}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} and t are also given which guarantee the strong convergence of the iteration processes.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.52 no.7
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• pp.355-362
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• 2003

The fault analysis problem of a distribution network has many difficulties comes from the unbalance of loads or networks and the lacks of load information. The unbalance of loads or networks make the fault location difficult when it use the classical sequence transformation. Moreover the amount of load in the distribution networks fluctuates with time. This paper introduces a recent fault location algorithm using iterative method which handle the unbalance of the problem. But, the fault location errors comes from the load fluctuations still left. For the real application of the new fault location algorithm in distribution networks, this paper studied the effect of the load fluctuations in the algorithm.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.1B
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• pp.99-104
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• 2000

In this paper, as a digital watermark we propose to use a chaotic sequence instead of the conventional Gaussian sequence. It is relatively easy to generate the chaotic sequence and is very sensitive to the change of initial value. The chaotic sequence adopted in this paper is a modified version of logistic map to give the sequence distribution of Chebyshev map. In the experiments, we applied the Gaussian sequence and chaotic sequence to wavelet coefficients of images to compare the similarity distribution. The results show that, as id the DCT-based watermarking system, the chaotic sequence is robust for various signal processing attacks, Moreover, the similarity variance is smaller than the Gaussian sequence for iterative experiments. It also shows a better performance for compression errors than the Gaussian sequence.