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A property of Ditzian–Totik second order moduli

Authors
Journal
Applied Mathematics Letters
0893-9659
Publisher
Elsevier
Publication Date
Volume
23
Issue
5
Identifiers
DOI: 10.1016/j.aml.2010.01.014
Keywords
  • Positive Linear Operators
  • Bernstein Type Operators
  • Ditzian–Totik Modulus
  • Voronovskaja Type Formulae

Abstract

Abstract For a function f ∈ C 2 [ 0 , 1 ] , we prove that lim t → 0 + ω φ 2 ( f , t ) t 2 = ‖ φ 2 f ″ ‖ , where ω φ 2 ( f , t ) denotes a Ditzian–Totik-type modulus of order 2. We apply this result to obtain an asymptotic property for positive linear operators related to Voronovskaja type formulae.

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