The Second Ditzian-Totik modulus revisited: refined estimates for positive linear operators

Heinz H. Gonska; Gancho T. Tachev

doi:10.33993/jnaat321-733

Authors

Heinz H. Gonska University of Duisburg, Germany
Gancho T. Tachev University of Architecture, Sofia, Bulgaria

DOI:

https://doi.org/10.33993/jnaat321-733

Keywords:

Bernstein operator, Ditzian-Totik moduli of smoothness, best constants, piecewise linear interpolation, Bernstein-Stancu operator, Gavrea operator

Abstract views: 254

Abstract

Direct theorems for approximation by positive linear operators in terms of the second order Ditzian-Totik modulus of smoothness are proved. Special emphasis is on the magnitude of the absolute constants. New results are obtained for Bernstein operators, for piecewise linear interpolation, for general Bernstein-Stancu operators and for those of Gavrea.

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References

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