Best local approximation and lateral differentiability

• Héctor H. Cuenya ^[1] ; David E. Ferreyra
  1. [1] Universidad Nacional de Río Cuarto

     Universidad Nacional de Río Cuarto

     Argentina

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 5, Nº. 1, 2013, págs. 81-99
• Idioma: inglés
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• Resumen

  • In this paper we give sufficient conditions over the differentiability of a function to assure existence of the best local approximant in Lp-spaces, 0 < p ≤ ∞. These conditions are weaker than those given in previous works. For p = 2 we show that, in certain way, they are also necessary. In addition, we characterize the best local approximant