• 대한수학회보
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• 제42권4호
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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.

• 대한수학회논문집
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• 제19권1호
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• pp.63-74
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• 2004

Suppose that X is a real Banach space, K is a nonempty closed convex subset of X and T : $K\;\rightarrow\;K$ is a uniformly continuous ${\phi}$-hemicontractive operator or a Lipschitz ${\phi}-hemicontractive$ operator. In this paper we prove that under certain conditions the three-step iteration methods with errors converge strongly to the unique fixed point of T. Our results extend the corresponding results of Chang [1], Chang et a1. [2], Chidume [3]-[7], Chidume and Osilike [9], Deng [10], Liu and Kang [13], [14], Osilike [15], [16] and Tan and Xu [17].

• 대한수학회논문집
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• 제26권1호
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• pp.23-35
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• 2011

In the present work we construct a composite implicit random iterative process with errors for a finite family of asymptotically nonexpansive random operators and discuss a necessary and sufficient condition for the convergence of this process in an arbitrary real Banach space. It is also proved that this process converges to the common random fixed point of the finite family of asymptotically nonexpansive random operators in the setting of uniformly convex Banach spaces. The present work also generalizes a recently established result in Banach spaces.

• 대한수학회보
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• 제46권4호
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• pp.627-644
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• 2009

The gauge-Uzawa method which has been constructed in [11] is a projection type method to solve the evolution Navier-Stokes equations. The method overcomes many shortcomings of projection methods and displays superior numerical performance [11, 12, 15, 16]. However, we have obtained only suboptimal accuracy via the energy estimate in [11]. In this paper, we study semi-discrete gauge-Uzawa method to prove optimal accuracy via energy estimate. The main key in this proof is to construct the intermediate equation which is formed to gauge-Uzawa algorithm. We will estimate velocity errors via comparing with the intermediate equation and then evaluate pressure errors via subtracting gauge-Uzawa algorithm from Navier-Stokes equations.

• 대한수학회지
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• 제45권6호
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• pp.1753-1767
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• 2008

Consider the nonparametric regression model $Y_{ni}\;=\;g(x_{ni})+{\epsilon}_{ni}$ ($1\;{\leq}\;i\;{\leq}\;n$), where g($\cdot$) is an unknown regression function, $x_{ni}$ are known fixed design points, and the correlated errors {${\epsilon}_{ni}$, $1\;{\leq}\;i\;{\leq}\;n$} have the same distribution as {$V_i$, $1\;{\leq}\;i\;{\leq}\;n$}, here $V_t\;=\;{\sum}^{\infty}_{j=-{\infty}}\;{\psi}_je_{t-j}$ with ${\sum}^{\infty}_{j=-{\infty}}\;|{\psi}_j|$ < $\infty$ and {$e_t$} are negatively associated random variables. Under appropriate conditions, we derive a Berry-Esseen type bound for the estimator of g($\cdot$). As corollary, by choice of the weights, the Berry-Esseen type bound can attain O($n^{-1/4}({\log}\;n)^{3/4}$).

• East Asian mathematical journal
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• 제29권2호
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• pp.189-205
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• 2013

Addition problems can be divided into the 'problem of quantity' which does not have the concept of object or unit, and the 'problem of number' which have the concept of object or unit. 'Additive property' is the factor which has to be considered in the former case. On the other hand, 'additive property' is not considered and meaningless in the latter case. However, this additive property is not emphasized in the elementary curriculum that mostly deals with quantitative problems, so related errors are occurred in actual life. In this study, we will investigate to the pre-service elementary teachers through the problems of deciding the additive property. The result shows that the pre-service elementary teachers' cognition of additive problems is insufficient. This study will provide focal points in the teacher education and the elementary education, and the clues for the operating programs through the information about the tendency of errors.

• 대한수학회논문집
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• 제25권4호
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• pp.571-581
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• 2010

Some convergence theorems for approximating to a common fixed point of an infinite family of strictly pseudocontractive mappings of Browder-Petryshyn type are proved in the setting of Banach spaces by using a new composite implicit iterative process with errors. The results presented in the paper generalize and improve the main results of Bai and Kim [1], Gu [4], Osilike [5], Su and Li [7], and Xu and Ori [8].

• 한국수학교육학회지시리즈A:수학교육
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• 제38권1호
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• pp.77-85
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• 1999

In this paper, we analyze strategies and error patterns in solving word problems of linear equation for middle school students. From a test conducted to the sampled 106 second grade middle school students, we obtain the following results: (1)The most difficult types of word problem are velosity and density related problems. The second one is length related problems and the easist one is number related problems. (2)Regardless of the types of word problem, the most familiar strategy is the constructing algebraic equations. However, the most successful strategy is the trial and error. (3)Most likely error patterns are the use of inadequate formulas and wrong trial and errors. Based on these results, a teaching program with various schema is developed and shown to be effective for mid level students in classroom.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제10권3호
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• pp.169-187
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• 2006

Ubiquitous errors in algebra like $(x+y)^2=x^2+y^2$ are a constant reminder that most students' manipulation of algebraic symbols has become detached from structural principles. The U.S. mathematics education community (NCTM, 2000) has responded by shying away from algebra as a structural study, preferring instead to ground meaning in empirical domains of reference. A new analysis of such errors shows that students' detachment from structural meaning stems from an inadequate structural curriculum, not from the inherent difficulty of adopting an abstract perspective on expressions and equations. A structural curriculum is outlined that preserves the possibility of students' engaging fully with algebra as both an empirical and a structural study.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제18권2호
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• pp.149-170
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• 2014

The Vietnamese language has a specific property related to the zero in the name-number system. This study was conducted to examine the impact of linguistic differences and of the zero's position in a number on a transcoding task (verbal number into Arabic number). Vietnamese children and French-speaking Belgian children, from grades 3 to 6, participated in the study. The success rate and the type of errors they made varied, depending on their grade and language. At Grade 4, Vietnamese children showed performances equivalent to Grade 6 Belgian children. Our results confirmed the support provided by language to the understanding and performances in a transcoding task. Results also showed that a syntactic zero is easier to manipulate than a lexical zero for Vietnamese children. The relative influence of language and the source of errors are discussed.