• Journal for History of Mathematics
• /
• v.30 no.1
• /
• pp.31-50
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.4
• /
• pp.299-312
• /
• 2006

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

• Research in Mathematical Education
• /
• v.17 no.2
• /
• pp.133-152
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.49 no.6
• /
• pp.1097-1110
• /
• 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
• /
• v.5 no.1
• /
• pp.1-8
• /
• 1997

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

• Journal of the Korean Mathematical Society
• /
• v.45 no.1
• /
• pp.289-300
• /
• 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
• /
• v.27 no.2
• /
• pp.153-163
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.15 no.2
• /
• pp.275-284
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.1
• /
• pp.75-83
• /
• 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
• /
• v.46 no.3
• /
• pp.337-343
• /
• 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.