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Global Smoothness Preservation by General Operators

  • George A. Anastassiou
  • Sorin G. Gal

Abstract

In this chapter we search the conditions under which global smoothness of a function f (as measured by its modulus of continuity) is preserved by the elements of general approximating sequences (L n f). As one consequence we obtain statements concerning the invariance of Lipschitz classes under operators of several types. An important tool in our approach is the least concave majorant of a modulus of continuity. Here we follow the basic study done by the first author, Cottin and Gonska [22].

Keywords

General Operator Banach Lattice Compact Interval Bernstein Polynomial Bernstein Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • George A. Anastassiou
    • 1
  • Sorin G. Gal
    • 2
  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA
  2. 2.Department of MathematicsUniversity of OradeaOradeaRomania

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