Weighted γ-K-functional and γ-modulus of smoothness on the semiaxis

• Zoltán Markó ^[1]
  1. [1] Budapest University of Technology and Economics

     Budapest University of Technology and Economics

     Hungría

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 7, Nº. 1, 2015, págs. 11-56
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper we investigate the γ-relative differentiation with the motivation of amending the order of the weighted polynomial approximation on the semiaxis for certain functions. By means of these tools, we give some definitions of generalized Sobolev spaces, K-functionals and moduli of smoothness. We estimate every one in terms of the others and, in the case of first order, we prove the equivalence. We show some possible applications and also other generalizations.