Document Type
Review
Abstract
In this research I will introduce a new method to an approximation in non-continuous functions space and estimate a degree of this approximation (Note that this function must be bounded) by define a new norm depending on union it together with a continuous function (I call it the compensation function) where the resulting functions from this union must be a continuous. This is possible for any continuous function but in this papers I will choose this function as an algebraic polynomial because our know of properties of polynomials in approximation theory Specifically, I will choose it as an interpolation polynomial according to Whitney's theorem in interpolation theory which we know precisely the degree of error when approximating our function by it according to Whitney's theorem, Also the range set for it, which is, as is the case in all polynomials, every real numbers, which will ensure that this set of images is closed to the subtraction process, which we will need in our work.
Keywords
non-continuous functions; bounded functions; compact sets; Whitney's theorem
Recommended Citation
Judy, Jawad K.
(2024)
"Interpolation in Non-Continuous Functions Spaces,"
Al-Qadisiyah Journal of Pure Science: Vol. 29
:
No.
1
, Article 3.
Available at:
https://doi.org/10.29350/2411-3514.1230
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