Abstract
In the present paragraph we shall give characterizations of elements of best approximation and some consequences of these characterizations in arbitrary (complex or real) normed linear spaces, and we shall apply them to various concrete spaces. Since we have *) $$ {L_G}\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {x\quad for\quad x \in G} \\ {\quad for\quad x \in \overline {G\backslash G,} } \end{array}} \right. $$ (1.1) for any linear subspace G of a normed linear space E, it will be sufficient to characterize the elements of best approximation of the elements \(x \in E\backslash \bar G\). In order to exclude the trivial case when such elements x do not exist, throughout the sequel by “linear subspace” G⊂E we shall understand “proper linear subspace G which is not dense in E”, that is, we shall assume, without special mention, that \(\bar G \ne E\).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.