• 한국수학사학회지
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• 제30권1호
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• pp.31-50
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• 2017

This study analyses on the history of uniform convergence, and discusses its educational implications. First, this study inspects 'overflowing of the Euclidean methodology' which was suggested by Lakatos as a cause of tardy appearance of uniform convergence, and reinterprets that cause in the perspective of 'symbolization'. Second, this study looks into the emergence of uniform convergence of Seidel and Weierstrass in this viewpoint of symbolization. As a result, of analysis, we come to know that the definition of uniform convergence had been changed into the theory of 'domain and graph' from that of 'point and function value' by the location change of the quantifier. As these results, this study puts forward an educational suggestion from an angle of epistemological obstacle, concept definition and concept image.

• 충청수학회지
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• 제19권4호
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• pp.299-312
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• 2006

In this paper, we introduce interior integral and prove uniform convergence theorems for the interior integral.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제17권2호
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• pp.133-152
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• 2013

In this research, we investigated students' understanding of the definitions of sequence of continuous functions and its uniform convergence. We selected three female and three male students out of the senior class of a university and conducted questionnaire surveys 4 times. We examined students' concept images of sequence of continuous functions and its uniform convergence and also how they approach to the right concept definitions for those through several progressive questions. Furthermore, we presented some suggestions for effective teaching-learning for the sequences of continuous functions.

• 대한수학회지
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• 제49권6호
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• pp.1097-1110
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• 2012

The convergence properties of extended negatively dependent sequences under some conditions of uniform integrability are studied. Some sufficient conditions of the weak law of large numbers, the $p$-mean convergence and the complete convergence for extended negatively dependent sequences are obtained, which extend and enrich the known results in the literature.

• Korean Journal of Mathematics
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• 제5권1호
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• pp.1-8
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• 1997

In this note, we study on fuzzy uniform convergences of sequences of fuzzy numbers, and sequences of fuzzy functions.

• 대한수학회지
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• 제45권1호
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• pp.289-300
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• 2008

For an array of dependent random variables satisfying a new notion of uniform integrability, weak laws of large numbers are obtained. Our results extend and sharpen the known results in the literature.

• Journal of the Korean Statistical Society
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• 제27권2호
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• pp.153-163
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• 1998

We investigate density estimation problem in the L$^{\infty}$ norm and show that the iii optimal minimax rates are achieved for smooth classes of weakly dependent stationary sequences. Our results are then applied to give uniform convergence rates for various problems including the Gibbs sampler.

• 대한수학회논문집
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• 제15권2호
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• pp.275-284
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• 2000

The existence and convergence theorems for fixed points of mappings of asymptotically nonexpansive type are established in Banach spaces with a weakly continuous duality mapping but without uniform convexity.

• 충청수학회지
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• 제24권1호
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• pp.75-83
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• 2011

In this paper the Baum-Katz law of large numbers for negatively orthant dependent random variables is studied. The complete convergence of negatively orthant dependent random variables under some conditions of uniform integrablity is also obtained.

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.337-343
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• 2006

In the present paper we shall prove that on a foundation *-semigroup S with an identity and with a locally bounded Borel measurable weight function ${\omega}$, the pointwise convergence and the uniform convergence of a sequence of ${\omega}$-bounded exponentially convex functions on S which are also continuous at the identity are equivalent.