Weighted Best Local ||.|| - Approximation in Orlicz Spaces

Abstract

In this paper we prove the existence of best multipoint local ||·||−approximation to a function f from an N−dimensional space SN for a suitable integer N. This problem is considered in an arbitrary Orlicz space for both the Luxemburg and the Orlicz norms when some bits of data are more important than others. For this purpose, we introduce the concept of || · ||−balanced integer.