Weighted best local || · ||−approximation in Orlicz spaces

H. Cuenya ^[1] ; S. Favier ^[2] ; F. Levis ^[1] ; C. Ridolf ^[2]
1. [1] Universidad Nacional de Río Cuarto
  
  Universidad Nacional de Río Cuarto
  
  Argentina
2. [2] Universidad Nacional de San Luis
  
  Universidad Nacional de San Luis
  
  Argentina
Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 2, Nº. 1, 2010, págs. 113-127
Idioma: inglés
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Resumen
- 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.