@article { author = {Anvar, Mohammad and Haddadi, Mohammad}, title = {Best simultaneous approximation in $L^{p}(S,X)$}, journal = {Mathematical Analysis and its Contemporary Applications}, volume = {4}, number = {1}, pages = {1-7}, year = {2022}, publisher = {Research & Science Group Ltd}, issn = {2716-9898}, eissn = {2716-9898}, doi = {10.30495/maca.2021.1935786.1019}, abstract = {As a counterpart to the best approximation in normed linear spaces, the best simultaneous approximation was introduced. In this paper, we shall consider relation between simultaneous proximinality $W$ in $X$ and $L^p(S,W)$ in $L^p(S,X)$ for $1\leq p\leq\infty$. Also, we consider the relation between w-simultaneous proximinality $W$ in $X$ and $L^p(S,W)$ in $L^p(S,X)$ for $1\leq p\leq\infty$.}, keywords = {Proximinal subspace,Simultaneous proximinal subspace,Simultaneous Chebyshev subspace,Reflexive subspace,Uniformly integrable}, url = {https://www.macajournal.com/article_686167.html}, eprint = {https://www.macajournal.com/article_686167_c4810b95b07be02773fec41b488ed601.pdf} }