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Direct estimates of the weighted simultaneous approximation by the Szász–Mirakjan operator

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Abstract

We establish direct estimates of the rate of weighted simultaneous approximation by the Szász–Mirakjan operator for smooth functions in the supremum norm on the non-negative semi-axis. We consider Jacobi-type weights. The estimates are stated in terms of appropriate moduli of smoothness or K-functionals.

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Acknowledgements

Professor H. Gonska turned my attention to the fact that J. Favard also introduced and studied the approximation properties of a general class of operators, to which \(S_n\) belongs. I am also thankful to Kiril Delev who provided me with Favard’s paper [11].

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, 5 James Bourchier Blvd., 1164, Sofia, Bulgaria

    Borislav R. Draganov

  2. Inst. of Mathematics and Informatics, Bulgarian Academy of Sciences, bl. 8 Acad. G. Bonchev Str., 1113, Sofia, Bulgaria

    Borislav R. Draganov

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  1. Borislav R. Draganov
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Correspondence to Borislav R. Draganov.

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This work was supported by Grant DN 02/14 of the Fund for Scientific Research of the Bulgarian Ministry of Education and Science.

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Draganov, B.R. Direct estimates of the weighted simultaneous approximation by the Szász–Mirakjan operator. Period Math Hung 83, 88–109 (2021). https://doi.org/10.1007/s10998-020-00370-x

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