Pointwise coproximinality in \(L^p(\mu, X)\)

Abstract

Let \(X\) be a Banach space, \(G\) be a closed subspace of \(X\), \((\Omega,\Sigma,\mu)\) be a \(\sigma\)-finite measure space, \(L(\mu,X)\) be the space of all strongly measurable functions from \(\Omega\) to \(X\), and \(L^{p}(\mu,X)\) be the space of all Bochner \(p-\)integrable functions from \(\Omega\) to \(X\). Discussing the relationship between the pointwise coproximinality of \(L(\mu, G)\) in \(L(\mu, X)\) and the pointwise coproximinality of \(L^{p}(\mu, G)\) in \(L^{p}(\mu, X)\) is the purpose of this paper.