Results in Mathematics

, Volume 16, Issue 3–4, pp 228–242 | Cite as

Direct and Converse Results on Weighted Simultaneous Approximation by the Method of Operators of Baskakov-Durrmeyer Type

  • Margareta Heilmann
  • Manfred W. Müller


We consider the n- th. operators of Baskakov-Durrmeyer type, which result from the classical Baskakov-type operators with weights p nk, if the values f(k/n) are replaced by the integral terms \((n - c)\int_{I} p_{nk} (t) f(t) dt \), where I denotes the corresponding interval which depends on the parameter c. For integrable functions the rate of weighted simultaneous approximation will be related to the Ditzian-Totik modulus of smoothness.


Bernstein Polynomial Linear Positive Operator Symmetry Argument Converse Result Weighted Modulus 
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Copyright information

© Birkhäuser Verlag, Basel 1989

Authors and Affiliations

  • Margareta Heilmann
    • 1
  • Manfred W. Müller
    • 1
  1. 1.Lehrstuhl Mathematik VIIIUniversität DortmundFed. Rep. of Germany

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