• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.661-672
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• 2009

In this paper, we introduce a modified three-step iteration scheme with errors for asymptotically nonexpansive mappings in the framework of uniformly convex Banach spaces. Weak and strong convergence theorems are established.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.137-147
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• 2012

In this paper we introduce some new double sequence spaces via ideal convergence and an Orlicz function in $n$-normed spaces and examine some properties of the resulting spaces.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.189-193
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• 1998

In this paper we construct a sequence of spaces which has Gromov-Hausdorff limit such that a geodesic in the limit space is not realized as a limit of geodesics in the spaces of the sequence. This contrasts with the result of Grove and Petersen in [1] where they proved otherwise for Alexandrov spaces with common curvature bounds.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.69-76
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• 2021

In this paper, we introduce the concept of ordered Banach space valued AP-Henstock integral and prove monotone convergence theorems for this integral.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.37-50
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• 2022

In this article we define and study the notions of $\mathcal{I}$-convergence and $\mathcal{I}$-Cauchy of triple sequences in the topology induced by random 2-normed spaces and prove some theorems based on them.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.621-629
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• 2019

In this paper, we present a local convergence analysis of a three point method with convergence order $1.839{\ldots}$ for approximating a locally unique solution of a nonlinear operator equation in setting of Banach spaces. Using weaker hypotheses than in earlier studies, we obtain: larger radius of convergence and more precise error estimates on the distances involved. Finally, numerical examples are used to show the advantages of the main results over earlier results.

• Journal of Korea Multimedia Society
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• v.21 no.2
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• pp.232-241
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• 2018

Operational Transformation (OT) algorithms for real-time collaborative editing systems are becoming increasingly important due to the increased demand for collaborative data processing. The operational transformation algorithm is a technique for real-time concurrency control and consistency maintenance with non-locking technique, and many studies have been conducted to overcome three issues of convergence, causality-prevention, and intention-prevention. However, previous work has the disadvantage of wasting memory by storing all operations that occurred during an edit operation in the history buffer to solve this problem. Therefore, we propose a memory-saving real-time collaborative editing system that maintains a constant memory space and concurrency control through a method of applying the valid-time to each user-generated operation in order to reduce memory waste. This system prevents long-term memory occupation of client-generated operations, thus it reduces the space and time complexity even with low-rate of collaboration work, so that the performance degradation avoids.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.2
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• pp.115-122
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• 2008

The effects of characteristic condition number on the convergence of preconditioned Euler equations were investigated. The two-dimensional preconditioned Euler equations adopting Choi and Merkle's preconditioning and the temperature preconditioning are considered. Preconditioned Roe's FDS scheme was adopted for spatial discretization and preconditioned LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of the Euler equations are strongly affected by the characteristic condition number, and there is an optimal characteristic condition number for a problem. The optimal characteristic condition numbers for the Choi and Merkle's preconditioning and temperature preconditioning are different.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.2
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• pp.123-130
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• 2008

The effects of characteristic condition number on the convergence of preconditioned Navier-Stokes equations were investigated. The two-dimensional preconditioned Navier-Stokes adopting Choi and Merkle's preconditioning and the temperature preconditioning are considered. Preconditioned Roe's FDS scheme was adopted for spatial discretization and preconditioned LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of the Navier-Stokes equations are strongly affected by the characteristic condition number. Also it is shown that the optimal characteristic condition numbers for viscous flows are larger than that in inviscid flows.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.6
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• pp.1-8
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• 2004

The objective of this study is convergence acceleration of multigrid Navier-Stokes solvers. This study has been performed to enhance the performance of preconditioned multi-stage time stepping method which is a popular smoother for the multigrid Navier-Stokes solvers. Comparative study on the convergence characteristics of the ADI and DDADI preconditioners has been conducted. It is shown that the DDADI preconditioner has better performance than the ADI by numerical tests on the 2-D compressible turbulent flows past airfoils. The Spalart-Allmaras turbulent model and the Baldwin-Lomax turbulent model have been compared with the multigrid calculations.