@Article{ATA-28-38,
author = {Sergei P. Sidorov},
title = {Estimates of Linear Relative n-widths in L^{p}[0, 1]},
journal = {Analysis in Theory and Applications},
year = {2012},
volume = {28},
number = {1},
pages = {38--48},
abstract = {In this paper we will show that if an approximation process {L_n}_nāN is shapepreservingrelative to the cone of all k-times differentiable functions with non-negative k-thderivative on [0,1], and the operators Ln are assumed to be of finite rank n, then the orderof convergence of D^kL_n f to D^k f cannot be better than $n^{ā2}$ even for the functions x^k, x^{k+1},x^{k+2} on any subset of [0,1] with positive measure. Taking into account this fact, we willbe able to find some asymptotic estimates of linear relative n-width of sets of differentiablefunctions in the space L^p[0,1], p ā N.},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2012.v28.n1.5},
url = {http://global-sci.org/intro/article_detail/ata/4539.html}
}