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

H.H. CUENYA; S. FAVIER; F.E. LEVIS; C.V. RIDOLFI

JAEN JOURNAL ON APPROXIMATION

Universidad de Jaén, Spain

Lugar: Jaen; Año: 2010 vol. 2 p. 113 - 127

1889-3066

In this paper we prove the existence of best multipoint local || . || -approximation to a function f from an N-dimensional space S_{N} 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.