Shape preserving properties of $ (\mathfrak{p}, \mathfrak{q}) $ Bernstein Bèzier curves and corresponding results over $ [a,b] $

Vinita Sharma; Asif Khan; Mohammad Mursaleen

doi:10.3934/mfc.2022041

Article Contents

2023, Volume 6, Issue 4: 691-703. Doi: 10.3934/mfc.2022041

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Shape preserving properties of $(\mathfrak{p}, \mathfrak{q})$ Bernstein Bèzier curves and corresponding results over $[a,b]$

1.
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2.
Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan

^*Corresponding author: Mohammad Mursaleen
^*Corresponding author: Mohammad Mursaleen

Received: April 2022

Revised: September 2022

Early access: October 2022

Published: November 2023

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Abstract

This article deals with shape preserving and local approximation properties of post-quantum Bernstein bases and operators over arbitrary interval $[a, b]$ defined by Khan and Sharma (Iran J Sci Technol Trans Sci (2021)). The properties for $(\mathfrak{p}, \mathfrak{q})$ -Bernstein bases and Bézier curves over $[a, b]$ have been given. A de Casteljau algorithm has been discussed. Further we obtain the rate of convergence for $(\mathfrak{p}, \mathfrak{q})$ -Bernstein operators over $[a, b]$ in terms of Lipschitz type space having two parameters and Lipschitz maximal functions.

Keywords:

$(\mathfrak{p}, \mathfrak{q})$ -Bernstein Bèzier curves,
de Casteljau algorithm,
Lipschitz maximal function.

Mathematics Subject Classification: Primary: 65D17; Secondary: 41A10, 41A25, 41A36.

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