Approximation by the modified $ \lambda $-Bernstein-polynomial in terms of basis function-Reference-Cited by-同舟云学术

Approximation by the modified $ \lambda $-Bernstein-polynomial in terms of basis function

Published:2024 Issue:2 Volume:9 Page:4409-4426
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Ayman-Mursaleen Mohammad¹,Nasiruzzaman Md.²,Rao Nadeem³,Dilshad Mohammad²,Nisar Kottakkaran Sooppy⁴

Affiliation:

1. School of Information and Physical Sciences, The University of Newcastle, University Drive, Callaghan, New South Wales 2308, Australia

2. Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 4279, Tabuk 71491, Saudi Arabia

3. Department of Mathematics, University Centre for Research and Development, Chandigarh University, Mohali-140413, Punjab, India

4. Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Abstract

<abstract><p>In this article by means of shifted knots properties, we introduce a new type of coupled Bernstein operators for Bézier basis functions. First, we construct the operators based on shifted knots properties of Bézier basis functions then investigate the Korovkin's theorem, establish a local approximation theorem, and provide a convergence theorem for Lipschitz continuous functions and Peetre's $ K $-functional. In addition, we also obtain an asymptotic formula of the type Voronovskaja.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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