The second order modulus revisited: remarks, applications, problems

Heiner Gonska; Ralitza K. Kovacheva

doi:10.33993/jnaat531-1410

Authors

Heiner Gonska University of Duisburg-Essen, Germany https://orcid.org/0000-0001-7448-2901
Ralitza K. Kovacheva Institute of Mathematics. Bulgarian Academy of Sciences, Bulgaria

DOI:

https://doi.org/10.33993/jnaat531-1410

Keywords:

second order modulus, degree of approximation, global smoothness preservation, Bernstein operators

Abstract views: 105

Abstract

Several questions concerning the second order modulus of smoothness are addressed in this note. The central part is a refined analysis of a construction of certain smooth functions by Zhuk and its application to several problems in approximation theory, such as degree of approximation and the preservation of global smoothness. Lower bounds for some optimal constants introduced by Sendov are given as well. We also investigate an alternative approach using quadratic splines studied by Sendov.

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