Document Type : Original Article

Authors

• Mohammad Valaei Anvar ¹
• Mohammad R Haddadi ²

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

• Proximinal subspace
• Simultaneous proximinal subspace
• Simultaneous Chebyshev subspace
• Reflexive subspace
• Uniformly integrable