scholarly journals A Case Study on Students' Concept Images of the Uniform Convergence of Sequences of Continuous Functions

2013 ◽  
Vol 17 (2) ◽  
pp. 133-152
Author(s):  
Moonja Jeong ◽  
Seong-A Kim
Keyword(s):  
Uniform Convergence ◽  
Continuous Functions ◽  
Concept Images ◽  
Convergence Of Sequences

scholarly journals XV.—On a Test for Continuity.

1908 ◽  
Vol 28 ◽  
pp. 249-258
Author(s):  
W. H. Young
Keyword(s):  
Uniform Convergence ◽  
Continuous Functions ◽  
Usual Method ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

§ 1. THE usual method of proving that a function defined as the limit of a sequence of continuous functions is continuous is by proving that the convergence is uniform. This method may fail owing to the presence of points at which the convergence is non-uniform although the limiting function is continuous. In such a case it would be necessary to apply a further test, e.g. that of Arzelà (“uniform convergence by segments”).In some cases the continuity may be proved directly by means of a totally different principle, without reference to modes of convergence at all. It is, in fact, a necessary and sufficient condition for the continuity of a function that it should be possible to express it at the same time as the limit of a monotone ascending and of a monotone descending sequence of continuous functions.

scholarly journals Statistical Convergence in Function Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Agata Caserta ◽  
Giuseppe Di Maio ◽  
Ljubiša D. R. Kočinac
Keyword(s):  
Uniform Convergence ◽  
Statistical Convergence ◽  
Statistical Approach ◽  
Metric Spaces ◽  
Function Spaces ◽  
Strong Uniform Convergence ◽  
Convergence Of Sequences

We study statistical versions of several classical kinds of convergence of sequences of functions between metric spaces (Dini, Arzelà, and Alexandroff) in different function spaces. Also, we discuss a statistical approach to recently introduced notions of strong uniform convergence and exhaustiveness.

scholarly journals The natural pseudo-distance as a quotient pseudo-metric, and applications

2015 ◽  
Vol 27 (3) ◽  
Author(s):  
Francesca Cagliari ◽  
Barbara Di Fabio ◽  
Claudia Landi
Keyword(s):  
Uniform Convergence ◽  
Similarity Measure ◽  
Compact Manifold ◽  
Continuous Functions ◽  
Point Of View ◽  
Space Of Continuous Functions ◽  
Morse Functions

AbstractThe natural pseudo-distance is a similarity measure conceived for the purpose of comparing shapes. In this paper we revisit this pseudo-metric from the point of view of quotients. In particular, we show that the natural pseudo-distance coincides with the quotient pseudo-metric on the space of continuous functions on a compact manifold, endowed with the uniform convergence metric, modulo self-homeomorphisms of the manifold. As applications of this result, the natural pseudo-distance is shown to be actually a metric on a number of function subspaces such as the space of topological embeddings, of isometries, and of simple Morse functions on surfaces.

scholarly journals λ-Statistical Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Vatan Karakaya ◽  
Necip Şimşek ◽  
Müzeyyen Ertürk ◽  
Faik Gürsoy
Keyword(s):  
Uniform Convergence ◽  
Pointwise Convergence ◽  
Statistical Convergence ◽  
Normed Spaces ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Convergence Of Sequences ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Convergent Sequences

We studyλ-statistically convergent sequences of functions in intuitionistic fuzzy normed spaces. We define concept ofλ-statistical pointwise convergence andλ-statistical uniform convergence in intuitionistic fuzzy normed spaces and we give some basic properties of these concepts.

scholarly journals Ideal convergent function sequences in random 2-normed spaces

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 557-567
Author(s):  
Ekrem Savaş ◽  
Mehmet Gürdal
Keyword(s):  
Uniform Convergence ◽  
Recent Work ◽  
Pointwise Convergence ◽  
Normed Spaces ◽  
Basic Properties ◽  
Convergence Of Sequences

In the present paper we are concerned with I-convergence of sequences of functions in random 2-normed spaces. Particularly, following the line of recent work of Karakaya et al. [23], we introduce the concepts of ideal uniform convergence and ideal pointwise convergence in the topology induced by random 2-normed spaces, and give some basic properties of these concepts.

scholarly journals On a Durrmeyer-type modification of the Exponential sampling series

2020 ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini
Keyword(s):  
Asymptotic Formula ◽  
Uniform Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Convergence Properties ◽  
Sampling Series ◽  
Quantitative Results ◽  
Uniformly Continuous

Abstract In this paper we introduce the exponential sampling Durrmeyer series. We discuss pointwise and uniform convergence properties and an asymptotic formula of Voronovskaja type. Quantitative results are given, using the usual modulus of continuity for uniformly continuous functions. Some examples are also described.

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