• East Asian mathematical journal
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• 제26권1호
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• pp.81-93
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• 2010

In this paper, a strong convergence theorem of multi-step iterative schemes with errors for asymptotically quasi-nonexpansive type nonself mappings is established in a real uniformly convex Banach space. Our results extend the corresponding results of Wangkeeree [12], Xu and Noor [13], Kim et al.[1,6,7] and many others.

• East Asian mathematical journal
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• 제19권1호
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• pp.103-111
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• 2003

In this paper, we will discuss some sufficient and necessary conditions for modified Ishikawa iterative sequence with mixed errors to converge to fixed points for asymptotically quasi-nonexpansive mappings in Banach spaces. The results presented in this paper extend, generalize and improve the corresponding results in Liu [4,5] and Ghosh-Debnath [2].

• 대한수학회지
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• 제35권1호
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• pp.191-205
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• 1998

In this paper, we prove that the Mann and Ishikawa iteration sequences with errors converge strongly to the unique solution of the equation x + Tx = f, where T is an m-accretive operator in uniformly smooth Banach spaces. Our results extend and improve those of Chidume, Ding, Zhu and others.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.465-478
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• 2006

In this paper, we introduce a new class of completely generalized strongly nonlinear quasivariational inequalities and establish its equivalence with a class of fixed point problems by using the resolvent operator technique. Utilizing this equivalence, we develop a three-step iterative scheme with errors, obtain a few existence theorems of solutions for the completely generalized non-linear strongly quasivariational inequality involving relaxed monotone, relaxed Lipschitz, strongly monotone and generalized pseudocontractive mappings and prove some convergence and stability results of the sequence generated by the three-step iterative scheme with errors. Our results include several previously known results as special cases.

• 한국수학사학회지
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• 제15권3호
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• pp.35-48
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• 2002

In this paper, we explore development of mathematical knowledge, especially calculus, non-Euclidean geometry, Euler's theorem, and the comparison of the number of elements in two infinite sets. And we analyze kinds of errors and the roles for errors with respect to increasing knowledge in mathematics.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.171-183
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• 2005

In this paper, we introduce and study a class of general strongly nonlinear quasivariational inequalities in Hilbert spaces. We prove the existence and uniqueness of solution and convergence of the perturbed the three-step iterative sequences with errors for this kind of general strongly nonlinear quasivariational inquality problems involving relaxed Lipschitz, relaxed monotone, and strongly monotone mappings. Our results extend, improve, and unify many known results due to Liu-Ume-Kang, Kim-Kyung, Zeng and others.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권4호
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• pp.357-369
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• 2007

Teachers and students' knowledge of zero was investigated through data collected from 16 preservice secondary mathematics teachers and 20 gifted secondary school students. Results showed that these teachers and students had an inadequate knowledge about zero. They exhibited a reluctance to accept zero as an attribute for classification, confusion as to whether or not zero is a number, and stable patterns of computational error. Although leachers and researchers have long recognized the value of analyzing student errors for diagnosis and remediation, students have not been encouraged to take advantage of errors as learning opportunities in mathematics instruction. The article suggests using errors as springboards for inquiry in action, discusses its potential contributions to mathematics instruction by analyzing students and preservice teachers errors related to zero.

• 대한수학회보
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• 제43권4호
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• pp.847-860
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• 2006

In this paper, some new convergence theorems of the modified Ishikawa and Mann iterative sequences with errors for asymptotically set-valued pseudocontractive mappings in uniformly smooth Banach spaces are given.

• 한국수학교육학회지시리즈A:수학교육
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• 제55권4호
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• pp.397-416
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• 2016

This study analyzed the quality of mathematics classes with observations using the instrument, MQI(Mathematical Quality of Instruction). Class recordings and interviews were conducted on 2 pre-service teachers and 4 in-service teachers. This study recorded and analyzed 3 or 4 classes for each mathematics teacher by using revised MQI. There were a total of 8 raters: 2 or 3 raters analyzed each class. MQI has four dimensions: Richness of the Mathematics, Working with Students and Mathematic, Errors and Imprecision, Student Participation in Meaning-Making and Reasoning. In the dimension of 'Richness of Mathematics', all teachers had good scores of 'explanations of teacher' but had lower scores of 'linking and connections', 'multiple procedures or solution methods' and 'developing mathematical generalizations.' In the dimension of 'Working with Students and Mathematics', two in-service teachers who have worked and having more experience had higher scores than others. In the dimension of 'Errors and Imprecision', all teachers had high scores. In the dimension of 'Student Participation in Meaning-Making and Reasoning', two pre-service teachers had contrast and also two in-service teachers who hadn't worked not long had contrast. Implications were deducted from finding to improving quality of mathematics classes.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.409-438
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• 2000

In this paper we develop a new procedure to control stepsize for Runge- Kutta methods applied to both ordinary differential equations and semi-explicit index 1 differential-algebraic equation In contrast to the standard approach, the error control mechanism presented here is based on monitoring and controlling both the local and global errors of Runge- Kutta formulas. As a result, Runge-Kutta methods with the local-global stepsize control solve differential of differential-algebraic equations with any prescribe accuracy (up to round-off errors)