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.
Publisher
Academia Romana Filiala Cluj
Reference52 articles.
1. A. Adell, I. de la Cal, Preservation of moduli of continuity for Bernstein-type operators, Manuscript 1993.
2. Preservation of Moduli of Continuity for Bernstein-Type Operators
3. G.A. Anastassiou, C. Cottin, H.H., Gonska, Global smoothness of approximating functions, Analysis 11 (1991), 43-57.
4. GLOBAL SMOOTHNESS OF APPROXIMATING FUNCTIONS
5. I.B. Bashmakova, On approximation by Hermite splines (Russian), In: Numerical Methodsin Boundary Value Problems of Mathemati- cal Physics(Meshvyz. Temat. Sb. Tr.), 5-7. Leningrad: Leningradskii Inzhemerno-Stroitelnyi Institut 1985.