Best simultaneous approximation in $L^{p}(S,X)$

Volume 4, Issue 1
Winter 2022
Pages 1-7

Document Type : Original Article

Authors

1 Department of Mathematics, Ayatollah Borujerdi University, Boroujerd, Iran

2 Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran

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

  • Receive Date 17 July 2021
  • Revise Date 30 October 2021
  • Accept Date 31 October 2021