Abstract
The aim of this paper is to present new non-asymptotic norm estimates in C[0,1] for the q-Bernstein operators B n,q in the case q > 1. While for 0 < q ≤ 1, ∥B n,q ∥ = 1 for all n ∈ ℕ, in the case q > 1, the norm ∥B n,q ∥ grows rather rapidly as n → +∞ and q → +∞. Both theoretical and numerical comparisons of the new estimates with the previously available ones are carried out. The conditions are determined under which the new estimates are better than the known ones.
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Acknowledgement
We would like to express our sincere gratitude to Mr. P. Danesh from Atilim University, Academic Writing and Advisory Centre, for his help in the preparation of the manuscript.
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Ostrovska, S., Özban, A.Y. (2013). Non-asymptotic Norm Estimates for the q-Bernstein Operators. In: Anastassiou, G., Duman, O. (eds) Advances in Applied Mathematics and Approximation Theory. Springer Proceedings in Mathematics & Statistics, vol 41. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6393-1_24
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DOI: https://doi.org/10.1007/978-1-4614-6393-1_24
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