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Approximation properties of <italic>λ</italic>-Bernstein operators.
- Source :
-
Journal of Inequalities & Applications . 3/16/2018, Vol. 2018 Issue 1, p1-1. 1p. - Publication Year :
- 2018
-
Abstract
- In this paper, we introduce a new type <italic>λ</italic>-Bernstein operators with parameter λ∈[−1,1]<inline-graphic></inline-graphic>, we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Finally, we give some graphs and numerical examples to show the convergence of Bn,λ(f;x)<inline-graphic></inline-graphic> to f(x)<inline-graphic></inline-graphic>, and we see that in some cases the errors are smaller than Bn(f)<inline-graphic></inline-graphic> to <italic>f</italic>. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10255834
- Volume :
- 2018
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Inequalities & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 128548686
- Full Text :
- https://doi.org/10.1186/s13660-018-1653-7