Article detail · 2025
On a new kind of λ-Bernstein-Kantorovich operators for univariate and bivariate functions
- Year
- 2025
- Type
- article
Data source split
- YÖKSİS YÖKSİS article record
- YÖKSİS venue Filomat
- Catalog match (ISSN) Filomat
- OpenAlex OpenAlex enrichment (abstract, citations, topics)
Abstract
English (OpenAlex)
This paper presents a novel class of ?-Bernstein operators, wherein the parameter ? ? [-1, 1]. An approximation theorem of the Korovkin type is explored, a local approximation theorem is established and an asymptotic formula of the Voronovskaja type is derived. In addition, the bivariate tensor product operators are built, some approximation properties are discussed, including an asymptotic theorem of the Voronovskaja type and the order of convergence in relation to Peetre?s K-functional. Finally, for certain continuous functions, numerical examples and plots to demonstrate our newly defined operators? convergence behavior are provided and there are also provided in comparison with the classical Kantorovich operators in terms of the approximation error.
Topics
- Approximation Theory and Sequence Spaces
- Iterative Methods for Nonlinear Equations
- Advanced Numerical Analysis Techniques
Primary topic Approximation Theory and Sequence Spaces