@Article{ATA-31-58,
author = {H. H. Cuenya and D. E. Ferreyra},
title = {$C^p$ Condition and the Best Local Approximation},
journal = {Analysis in Theory and Applications},
year = {2017},
volume = {31},
number = {1},
pages = {58--67},
abstract = {<p style="text-align: justify;">In this paper, we introduce a condition weaker than the $L^p$ differentiability, which we call $C^p$ condition. We prove that if a function satisfies this condition at a point, then there exists the best local approximation at that point. We also give a necessary and sufficient condition for that a function be $L^p$ differentiable. In addition, we study the convexity of &nbsp;the set of cluster points of the net of best approximations of $f$, $\{P_\epsilon(f)\}$ as $\epsilon \to 0$.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2015.v31.n1.5},
url = {http://global-sci.org/intro/article_detail/ata/4622.html}
}