Abstract
Let E be a closed set with inf E = a and sup E = b, and k be a positive integer. Let f : E → Rbe such that the k-th Peano derivative of f relative to E, f (k) (x, E), exists. It is proved under certain condition on the function f, that an extension F : [a, b] → Rof f exists such that the ordinary derivative of F of order k, F <k> (x) exists on [a, b] and is continuous on [a, b], and f <> (x, E) = F <i> (x) on E, for i = 1, 2, &, k.
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Mukhopadhyay, S., Ray, S. On Extending Peano Derivatives. Acta Mathematica Hungarica 89, 327–346 (2000). https://doi.org/10.1023/A:1006718606620
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DOI: https://doi.org/10.1023/A:1006718606620