Cheney and Sharma type operators and Korovkin test functions

• Jorge Bustamante ^[1] ; Miguel A. Jiménez Pozo ^[1]
  1. [1] Benemérita Universidad Autónoma de Puebla

     Benemérita Universidad Autónoma de Puebla

     México

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 4, Nº. 2, 2012, págs. 137-155
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Hereby we define a class of sequences of positive linear operators that contains the ones introduced by Cheney and Sharma in 1964, as well as several others based upon the same idea of the classical Meller-K¨onig and Zeller operators. The sequences included in this class share the property of being associated to functional differential equations which let us the possibility of explicitly evaluating the Korovkin test functions as solutions of the equations. After a unified study of different approximation problems for sequences within this class, we apply the constructed theory to explicit sequences of operators from which we obtain old and new results as well.