Abstract
We consider the Durrmeyer modification of the Szász-Mirakjan operators. The rate of simultaneous approximation by linear combinations is related to the Ditzian-Totik modulus of smoothness. We prove a direct and a corresponding inverse theorem and, partly as a corollary, an equivalence result.
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Dedicated to the memory of Lothar Collatz
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Heilmann, M. (1992). Rate of Approximation of Weighted Derivatives by Linear Combinations of SMD Operators. In: Braess, D., Schumaker, L.L. (eds) Numerical Methods in Approximation Theory, Vol. 9. ISNM 105: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 105. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8619-2_6
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DOI: https://doi.org/10.1007/978-3-0348-8619-2_6
Publisher Name: Birkhäuser, Basel
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