Grüss-type inequalities for positive linear operators with second order moduli

Authors

  • Heiner Gonska University of Duisburg-Essen, 47048 Duisburg, Germany Author
  • Gancho Tachev University of Architecture, 1046 Sofia, Bulgaria Author

Keywords:

Grüss-type inequality, positive linear operators, Bernstein operator, variation-diminishing Schoenberg-splines, second order modulus of smoothness

Subjects:

41A36, 41A17, 41A25, 39B62

Abstract

We prove two Grüss-type inequalities for positive linear operator approximation, i.e., inequalities explaining thenon-multiplicativity of such mappings. Instead of the least concave majorant of the first order modulus of continuity, we employ second order moduli ofsmoothness and show in the case of the classical Bernstein operators that in certain cases this leads to better results than those obtained earlier.

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Published

2011-10-15

Issue

Vol. 63 No. 4 (2011): Vol. 63, Issue 4

Section

Articles

License

Copyright (c) 2011 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.