@article{Ayman-Mursaleen2024, 
author = {Mohammad Ayman-Mursaleen and Md. Nasiruzzaman and Nadeem Rao and Mohammad Dilshad and Kottakkaran Sooppy Nisar},
title = {Approximation by the modified    λ-Bernstein-polynomial in terms of basis function},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {4409-4426},
keywords = {Bernstein-polynomial, λ-Bernstein-polynomial, Bézier basis function, shifted knots, modulus of continuity, Lipschitz maximal functions, Peetre's K-functional},
url = {https://www.sciopen.com/article/10.3934/math.2024217},
doi = {10.3934/math.2024217},
abstract = {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.}
}