• 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.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.513-520
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• 2014

We study numerical methods to obtain the stationary probabilities of continuous-time Markov chains whose embedded chains are periodic. The power method is applied to the balance equations of the periodic embedded Markov chains. The power method can have the convergence speed of exponential rate that is ambiguous in its application to original continuous-time Markov chains since the embedded chains are discrete-time processes. An illustrative example is presented to investigate the numerical iteration of this paper. A numerical study shows that a rapid and stable solution for stationary probabilities can be achieved regardless of periodicity and initial conditions.

• Korean Journal of Remote Sensing
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• v.24 no.1
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• pp.79-89
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• 2008

Irregular temporal sampling is a common feature of geophysical and biological time series in remote sensing. This study proposes an on-line system for reconstructing observation image series contaminated by noises resulted from mechanical problems or sensing environmental condition. There is also a high likelihood that during the data acquisition periods the target site corresponding to any given pixel may be covered by fog or cloud, thereby resulting in bad or missing observation. The surface parameters associated with the land are usually dependent on the climate, and many physical processes that are displayed in the image sensed from the land then exhibit temporal variation with seasonal periodicity. A feedback system proposed in this study reconstructs a sequence of images remotely sensed from the land surface having the physical processes with seasonal periodicity. The harmonic model is used to track seasonal variation through time, and a Gibbs random field (GRF) is used to represent the spatial dependency of digital image processes. The experimental results of this simulation study show the potentiality of the proposed system to reconstruct the image series observed by imperfect sensing technology from the environment which are frequently influenced by bad weather. This study provides fundamental information on the elements of the proposed system for right usage in application.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.737-746
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• 1999

We consider a class of discrete parameter processes on a locally compact Banach space S arising from successive compositions of strictly stationary random maps with state space C(S,S), where C(S,S) is the collection of continuous functions on S into itself. Sufficient conditions for stationary solutions are found. Existence of pth moments and convergence of empirical distributions for trajectories are proved.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1157-1162
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• 2019

In this paper, we extend the study of general convergence theorems for the Picard iteration of Proinov contraction from the class of continuous mappings to the class of discontinuous mappings. As a by product we provide a new affirmative answer to the open problem posed in [20].

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.433-441
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• 2012

We adapt the concept of shrinking projection method of Takahashi et al. [J. Math. Anal. Appl. 341(2008), 276-286] to the iteration scheme studied by Kim and Lee [Kyungpook Math. J. 48(2008), 685-703] for two relatively weak nonexpansive mappings. By letting one of the two mappings be the identity mapping, we also obtain strong convergence theorems for a single mapping with two types of computational errors. Finally, we improve Kim and Lee's convergence theorem in the sense that the same conclusion still holds without the uniform continuity of mappings as was the case in their result.

• Journal of Information Processing Systems
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• v.11 no.4
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• pp.616-629
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• 2015

A mobile terminal will expect a number of handoffs within its call duration. In the event of a mobile call, when a mobile node moves from one cell to another, it should connect to another access point within its range. In case there is a lack of support of its own network, it must changeover to another base station. In the event of moving on to another network, quality of service parameters need to be considered. In our study we have used the Markov decision process approach for a seamless handoff as it gives the optimum results for selecting a network when compared to other multiple attribute decision making processes. We have used the network cost function for selecting the network for handoff and the connection reward function, which is based on the values of the quality of service parameters. We have also examined the constant bit rate and transmission control protocol packet delivery ratio. We used the policy iteration algorithm for determining the optimal policy. Our enhanced handoff algorithm outperforms other previous multiple attribute decision making methods.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.485-490
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• 1998

We consider a class of discrete parameter processes on a locally compact Polish space $S$ arising from successive compositions of strictly stationary Markov random maps on $S$ into itself. Sufficient conditions for the existence of the stationary solution and the weak convergence of the distributions of $\{\Gamma_n \Gamma_{n-1} \cdots \Gamma_0x \}$ are given.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.227-234
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• 1996

Consider nonlinear autoregressive processes of order 1 defined by the random iteration $$ (1) X_{n + 1} = f(X_n) + \epsilon_{n + 1} (n \geq 0) $$ where f is real-valued Borel measurable functin on $R^1, {\epsilon_n : n \geq 1}$ is an i.i.d.sequence whose common distribution F has a non-zero absolutely continuous component with a positive density, $E$\mid$\epsilon_n$\mid$ < \infty$, and the initial $X_0$ is independent of ${\epsilon_n : n > \geq 1}$.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.11
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• pp.28-35
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• 2013

The Krylov-Schur algorithm has been applied to reveal the eigen-properties of the wave guide having the square cross section. The eigen-matrix equation has been constructed from FEM with the basis function of the tangential edge-vectors of the triangular element. This equation has been treated firstly with Arnoldi decomposition to obtain a upper Hessenberg matrix. The QR algorithm has been carried out to transform it into Schur form. The several eigen values satisfying the convergent condition have appeared in the diagonal components. The eigen-modes for them have been calculated from the inverse iteration method. The wanted eigen-pairs have been reordered in the leading principle sub-matrix of the Schur matrix. This sub-matrix has been deflated from the eigen-matrix equation for the subsequent search of other eigen-pairs. These processes have been conducted several times repeatedly. As a result, a few primary eigen-pairs of TE and TM modes have been obtained with sufficient reliability.