• Honam Mathematical Journal
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• v.42 no.1
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• pp.161-173
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• 2020

We introduce statistically localized sequences in 2-normed spaces and give some main properties of statistically localized sequences. Also, we prove that a sequence is statistically Cauchy sequence if and only if its statistical barrier is equal to zero. Moreover, we define the uniformly statistically localized sequences on 2-normed spaces and investigate its relationship with statistically Cauchy sequences.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.255-275
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• 2022

In this paper, we introduce a new system of set-valued variational inclusion problems in semi-inner product spaces. We use resolvent operator technique to propose an iterative algorithm for computing the approximate solution of the system of set-valued variational inclusion problems. The results presented in this paper generalize, improve and unify many previously known results in the literature.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.299-318
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• 2023

This article devises an exponentially fitted method for the numerical solution of two parameter singularly perturbed parabolic boundary value problems. The proposed scheme is able to resolve the two lateral boundary layers of the solution. Error estimates show that the constructed scheme is parameter-uniformly convergent with a quadratic numerical rate of convergence. Some numerical test examples are taken from recently published articles to confirm the theoretical results and demonstrate a good performance of the current scheme.

• East Asian mathematical journal
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• v.24 no.1
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• pp.35-43
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• 2008

Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let ${\{T_i\}}^N_{i=1}$ be N nonexpansive self-mappings of K with $F\;=\;{\cap}^N_{i=1}F(T_i)\;{\neq}\;{\theta}$ (here $F(T_i)$ denotes the set of fixed points of $T_i$). Suppose that one of the mappings in ${\{T_i\}}^N_{i=1}$ is semi-compact. Let $\{{\alpha}_n\}\;{\subset}\;[{\delta},\;1-{\delta}]$ for some ${\delta}\;{\in}\;(0,\;1)$ and $\{{\beta}_n\}\;{\subset}\;[\tau,\;1]$ for some ${\tau}\;{\in}\;(0,\;1]$. For arbitrary $x_0\;{\in}\;K$, let the sequence {$x_n$} be defined iteratively by $\{{x_n\;=\;{\alpha}_nx_{n-1}\;+\;(1-{\alpha}_n)T_ny_n,\;\;\;\;\;\;\;\;\; \atop {y_n\;=\;{\beta}nx_{n-1}\;+\;(1-{\beta}_n)T_nx_n},\;{\forall}_n{\geq}1,}$, where $T_n\;=\;T_{n(modN)}$. Then {$x_n$} convergence strongly to a common fixed point of the mappings family ${\{T_i\}}^N_{i=1}$. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of ${\beta}_n\;{\equiv}\;1$ or N=1 are also new.

• The Journal of Korea Robotics Society
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• v.18 no.2
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• pp.189-196
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• 2023

An abdominal brace is a recommended treatment for patients with lumbar spinal disorders. However, due to the nature of the static brace, it uniformly compresses the lumbar region, which can weaken the lumbar muscles or create a psychological dependence that worsens the condition of the spine when worn for an extended period of time. Due to these issues, doctors limit the wearing time when prescribing it to patients. In this paper, we propose a device that can dynamically provide abdominal pressure and support according to the lumbar motion. The proposed device is a wearable robot in the form of a brace, with actuators and a driving unit mounted on the brace. To enhance wearability and reduce the weight of the device, worm gears actuator and a multi-pulley mechanism were adopted. Based on the spinal motion of the wearer measured by the Inertia measurement unit sensors, the drives wire by driving pulley, which provide tension to the multi-pulley mechanism on both sides, dynamically tightening or loosening the device. Finally, the device can dynamically provide abdominal pressure and support. We describe the hardware and system configuration of the device and demonstrate its potential through basic control experiments.

• Convergence Security Journal
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• v.8 no.3
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• pp.57-64
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• 2008

The Security of digital images has become increasingly more important in highly computerized and interconnected world. Therefore, The chaos-based encryption algorithms have suggested some new and efficient ways to develop secure image encryption method. This paper is described for the point at issue in all chaos-based encryption method for distribution of a chaotic signals. It has a method for generation of uniformly distributed chaotic signals that we designed secure algorithm of multi-parameter chaotic systems. So we are present validity of the theoretical models for results of image encryption and decryption for proposed method.

• Journal of the Korean Society of Industry Convergence
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• v.4 no.1
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• pp.41-49
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• 2001

This study developed signal optimization algorithm by analyzing vehicle arrival patterns. The major principle of signal optimization is dissipate all queueing vehicle in 1cycle and assign delay time uniformly for all approaches. For this, this study used optimal green time and surplus green time. Optimal green time calculated by estimated traffic volume from vehicle arrival model. Surplus green time defined as the gap of optimal green time and queue dissipated time. And alternative cycle has minimum surplus green time was selected as the optimal cycle. Finally, total delay and average delay per vehicle can be calculated by using queueing theory.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.185-201
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• 2014

In this paper, we construct a numerical method to solve singularly perturbed one-dimensional parabolic convection-diffusion problems. We use Euler method with uniform step size for temporal discretization and exponential-spline scheme on spatial uniform mesh of Shishkin type for full discretization. We show that the resulting method is uniformly convergent with respect to diffusion parameter. An extensive amount of analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter. The obtained numerical results show that the method is efficient, stable and reliable for solving convection-diffusion problem accurately even involving diffusion parameter.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.59-68
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• 2009

In this paper we present an iterative scheme for finding a common element of the set of zero points of accretive mappings and the set of fixed points of nonexpansive mappings in Banach spaces. By using viscosity approximation methods and under suitable conditions, some strong convergence theorems for approximating to this common elements are proved. The results presented in the paper improve and extend the corresponding results of Kim and Xu [Nonlinear Anal. TMA 61 (2005), 51-60], Xu [J. Math. Anal. Appl., 314 (2006), 631-643] and some others.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.129-137
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• 2010

In this paper, we introduce and study a system of nonlinear set-valued implicit variational inclusions (SNSIVI) with relaxed cocoercive mappings in real Banach spaces. By using resolvent operator technique for M-accretive mapping, we construct a new class of iterative algorithms for solving this class of system of set-valued implicit variational inclusions. The convergence of iterative algorithms is proved in q-uniformly smooth Banach spaces. Our results generalize and improve the corresponding results of recent works.