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Iterated Bernstein Polynomial Approximations

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Fixed Point Theory in Metric Spaces

Abstract

Kelisky and Rivlin [7] proved that each Bernstein operator \(B_n\) is a weaky Picard operator (WPO). Moreover, given \(n\in \mathbb {N}\) and \(\varphi \in C([0,1];\mathbb {R})\),

$$ \lim _{j\rightarrow \infty }(B_n^j\varphi )(t) = \varphi (0) + (\varphi (1)- \varphi (0))t, \quad t \in [0, 1]. $$

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Correspondence to Praveen Agarwal .

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Agarwal, P., Jleli, M., Samet, B. (2018). Iterated Bernstein Polynomial Approximations. In: Fixed Point Theory in Metric Spaces. Springer, Singapore. https://doi.org/10.1007/978-981-13-2913-5_10

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