• 대한수학회지
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• 제36권6호
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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.

• 대한수학교육학회지:수학교육학연구
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• 제25권3호
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• pp.281-302
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• 2015

본 연구에서는 국가수준 학업성취도 서답형 문항의 문제해결 과정에서 나타나는 오류를 살펴보기 위하여 236개 학교 8007명의 답안지를 추출하여 분석하였다. 분석에 사용한 문항은 국가수준 학업성취도 평가 중학교 수학 서답형 문항으로 내용 영역은 '문자와 식', '함수'이고 행동 영역은 '문제해결'과 '계산'이다. 두 문항 모두 주어진 문제 상황에 알맞은 식을 세우고 조건에 맞는 결과를 산출하는 문제이다. 분석 결과 각 문항에 따라 문제 상황을 파악하여 식을 세우고, 풀며, 결과를 기술하는 세가지 과정에서 다양한 오류들이 나타났다. 본 연구에서는 이에 대한 원인을 추론하여 교수학적 시사점을 이끌어 내고자 하였다.

• 대한수학회보
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• 제39권1호
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• pp.23-31
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• 2002

A scale parameter is the principal parameter to be estimated, since it corresponds to one of the main reliability characteristics, namely the average time to failure. To provide robustness of scale estimators to gross errors in the data, we apply the Huber minimax approach in time to failure models of the statistical reliability theory. The minimax valiance estimator of scale is obtained in the important particular case of the exponential distribution.

• 대한수학회보
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• 제53권1호
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• pp.247-262
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• 2016

We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations (VIEs). We provide a rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

• 대한수학회보
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• 제33권3호
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• pp.377-383
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• 1996

We consider in this paper the following nonlinear regression model $$ (1.1) y_t = f(x_t, \theta_o) + \in_t, t = 1, \ldots, n, $$ where $y_t$ is the tth response, $x_t$ is m-vector imput variable, $\theta_o$ is a p-vector of unknown parameter belong to a parameter space $\Theta, f:R^m \times \Theta \ to R^1$ is a nonlinear known function, and $\in_t$ are independent unobservable random errors with finite second moment.

• 대한수학회보
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• 제39권3호
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• pp.455-469
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• 2002

The Purpose Of this Paper is to introduce the concept of a class of strictly successively hemicontractive mappings and construct certain stable and almost stable iteration procedures for the iterative approximation of fixed points for asymptotically nonexpansive and strictly successively hemicontractive mappings in Banach spaces.

• 대한수학회보
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• 제39권3호
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• pp.389-399
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• 2002

We prove that the results of Chang, Park and Cho in ［1］ concerning the iterative approximation of asymptotically pseudocontractive maps with bounded ranges can be extended to a certain class of asymptotically pseudocontractive maps whose ranges need not be bounded.

• 대한수학회보
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• 제49권4호
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• pp.775-785
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• 2012

Some errors in literatures are pointed out and corrected. A generalization of Ostrowski type inequalities for functions whose derivatives in absolute value are s-convex in the second sense is established. Special cases are discussed.

• 대한수학회보
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• 제47권6호
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• pp.1259-1268
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• 2010

In this paper, we consider an implicit iterative process with errors for an in nite family of strict pseudocontractions. Strong convergence theorems are established in the framework of Banach spaces. The results presented in this paper improve and extend the recent ones announced by many others.

• 대한수학회지
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• 제40권6호
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• pp.1075-1083
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• 2003

The purpose of this paper is to investigate the piecewise wise polynomial approximation for the curved boundary. We analyze the error of an approximated solution due to this approximation and then compare the approximation errors for the cases of polygonal and piecewise polynomial approximations for the curved boundary. Based on the results of analysis, p-version numerical methods for solving Dirichlet's problems are applied to any smooth curved domain.