Approximation by Bézier type associated shifted knots of (λ, q)-Bernstein operators
In this article, we introduce the (?, q)-Bernstein operators associated with B?zier basis functions using the features of shifted knots. We first construct the (?, q)-Bernstein operators using shifted knot polynomials that are connected by a B?zier basis function. We then look into Korovkin?s theorem, prove a local approximation theorem, and obtain the convergence theorem for Peetre?s K-functional and Lipschitz continuous functions. The Voronovskaja type asymptotic formula is finally found in the concluding section of this paper.
Authors
- Ahmed Alamer (ORCID: https://orcid.org/0000-0002-1249-6424)
- Nawal Odah Al-Atawi (ORCID: https://orcid.org/0000-0003-4027-2804)
- Md. Nasiruzzaman (ORCID: https://orcid.org/0000-0003-4823-0588)
- Esmail Alshaban (ORCID: https://orcid.org/0009-0000-0385-2557)
- Ravi Kumar (ORCID: https://orcid.org/0009-0001-1155-3503)
- Mohammad Mursaleen (ORCID: https://orcid.org/0000-0003-4128-0427)
- Adel Alatawi (ORCID: https://orcid.org/0009-0000-8154-0858)
Institutions
- China Medical University (TW)
- Patna University (IN)
- China Medical University Hospital (TW)
- University of Tabuk (SA)
- Saveetha University (IN)
Publication Details
- Journal
- Filomat
- Published
- 2025-01-01
- DOI
- https://doi.org/10.2298/fil2503997n
- Primary Topic
- Approximation Theory and Sequence Spaces
- Type
- article
- Field-Weighted Citation Impact
- 0.00