Abstract
We prove asymptotic evaluations for univariate and multivariate positive linear operators. Our proofs are different from what has been used so far. As applications of our results, we find the full asymptotic evaluation for the iterates of the univariate Cesàro and Volterra operators. Moreover, we find asymptotic evaluations for the iterates of multivariate Cesàro and Volterra type operators on the k-dimensional unit cube, k-dimensional unit triangle, etc.
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Acknowledgements
We would like to express our gratitude to the two reviewers for their very careful reading of the manuscript and their many valuable and constructive comments that have improved the final version of the paper.
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Communicated by Wolfgang Dahmen.
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Popa, D. Asymptotic Evaluations for Some Sequences of Positive Linear Operators. Constr Approx 50, 293–321 (2019). https://doi.org/10.1007/s00365-018-9449-z
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DOI: https://doi.org/10.1007/s00365-018-9449-z
Keywords
- Korovkin approximation theorem
- Positive linear operators
- Asymptotic evaluations for univariate and multivariate positive operators
- Iterates
- Cesàro and Volterra operator