Year: 2015
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 1 : pp. 58–67
Abstract
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 the set of cluster points of the net of best approximations of $f$, $\{P_\epsilon(f)\}$ as $\epsilon \to 0$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2015.v31.n1.5
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 1 : pp. 58–67
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Best $L^p$ approximation local approximation $L^p$ differentiability.