Note on Jakimovski-Leviatan operators preserving \(e^{-x}\). (English) Zbl 1524.41008
Summary: In the present article, a modification of Jakimovski-Leviatan operators is presented which reproduce constant and \(e^{-x}\) functions. We prove uniform convergence order of a quantitative estimate for the modified operators. We also give a quantitative Voronovskya type theorem.
MSC:
| 41A10 | Approximation by polynomials |
| 41A25 | Rate of convergence, degree of approximation |
| 41A36 | Approximation by positive operators |
Keywords:
Jakimovski-Leviatan operators; exponential functions; quantitative asymptotic formula; uniform convergence; Voronovskya-type theoremReferences:
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