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The narrow border between a continuous function and a discontinuous function

Volume 5, Issue 3, June 2020    |    PP. 32-43    |PDF (824 K)|    Pub. Date: September 25, 2020
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Author(s)
Alicia C. Sánchez, "Santa Eulalia" High School. Spain

Abstract
The RAFU functions have been studied in [1, 2, 3, 4, 5 and 6]. They are useful in Approximation Theory to approach continuous functions and to reconstruct continuous functions. In this work we will use the RAFU functions to turn a discontinuous function into a continuous function. We will show the explicit expression of a sequence of continuous functions that converges to a discontinuous function given except at its discontinuity points. The paper shows examples for different types of discontinuities.

Keywords
RAFU functions; continuous functions; discontinuous functions.

Cite this paper
Alicia C. Sánchez, The narrow border between a continuous function and a discontinuous function, SCIREA Journal of Mathematics. Vol. 5 , No. 3 , 2020 , pp. 32 - 43 .

References

[ 1 ] E. Corbacho. Uniform approximation with radical functions. SeEMA Journal 58 (1). 97-122. April 2012.
[ 2 ] E. Corbacho. A RAFU linear space uniformly dense in C[a, b]. Applied General Topology 14 (1). 53-60. 2013.
[ 3 ] E. Corbacho. The RAFU method on approximation. LAP Lambert Academic Publishing. 2015.
[ 4 ] E. Corbacho. Approximation in different smoothness spaces with the RAFU method. Applied General Topology 15 (2). 221--228. 2014
[ 5 ] E. Corbacho. Simultaneous approximation with the RAFU method. Journal of Mathematical Inequalities 10 (1). 219-231. 2016
[ 6 ] E Corbacho. Uniform reconstruction of continuous functions with the RAFU method. Applied General Topology 18 (2). 361-375. 2017.