Gonska Progress in Global Smoothness Preservation

George A. Anastassiou and Sorin G. Gal
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George A. Anastassiou: University of Memphis, Department of Mathematical Sciences
Sorin G. Gal: University of Oradea, Department of Mathematics

Chapter 18 in Approximation Theory, 2000, pp 451-471 from Springer

Abstract: Abstract Here global smoothness is mainly expressed by the Peetre K-functional of order s ≥1, defined by $$ \begin{gathered} K_S \left( {f,\delta } \right): = K\left( {f;\delta ;C\left( {\left[ {0,1} \right]} \right),C^s \left( {\left[ {0,1} \right]} \right)} \right) \hfill \\ : = \inf \left\{ {\parallel f - g\parallel _\infty :g \in C^s \left( {\left[ {0,1} \right]} \right)} \right\} \hfill \\ \end{gathered} $$ where f ∈ C([0,1]),δ ≥0, and ∥ · ∥ ∞is the supremum norm.

Keywords: Univariate Operator; Supremum Norm; Bernstein Polynomial; Positive Linear Operator; Bernstein Operator (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-1-4612-1360-4_18

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