On simultaneous approximation

Abstract

In this paper first we give two different definitions for best simultaneous $%L_{\text{p }}$ approximation to $n$ functions and study the relation betweenbest simultaneous approximation and best $L_{\text{p }}$approximations tothe arithmetic mean of $n$ functions. In addition we consider the definitionand the theorem about the simultaneous approximation to $n$ ($n$ odd)functions in the ''sum'' norm .