Iterated Bernstein Polynomial Approximations

Praveen Agarwal (), Mohamed Jleli and Bessem Samet
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Praveen Agarwal: Anand International College of Engineering, Department of Mathematics
Mohamed Jleli: King Saud University, Department of Mathematics, College of Sciences
Bessem Samet: King Saud University, Department of Mathematics, College of Sciences

Chapter Chapter 10 in Fixed Point Theory in Metric Spaces, 2018, pp 155-164 from Springer

Abstract: Abstract Kelisky and Rivlin [7] provedBernstein polynomial that each Bernstein operator $$B_n$$ is a weaky Picard operator (WPO). Moreover, given $$n\in \mathbb {N}$$ and $$\varphi \in C([0,1];\mathbb {R})$$ , $$ \lim _{j\rightarrow \infty }(B_n^j\varphi )(t) = \varphi (0) + (\varphi (1)- \varphi (0))t, \quad t \in [0, 1]. $$

Date: 2018
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DOI: 10.1007/978-981-13-2913-5_10

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