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Iterated Bernstein Polynomial Approximations

  • Praveen Agarwal
  • Mohamed Jleli
  • Bessem Samet
Chapter

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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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsAnand International College of EngineeringJaipurIndia
  2. 2.Department of Mathematics, College of SciencesKing Saud UniversityRiyadhSaudi Arabia

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