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Erschienen in:
2019 | OriginalPaper | Buchkapitel
Modified Post-Widder Operators Preserving Exponential Functions
verfasst von : Vijay Gupta, Vinai K. Singh
Erschienen in: Advances in Mathematical Methods and High Performance Computing
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Abstract
The paper considers a modification \(\widetilde {P}_n\) of the Post-Widder operators, which contains two auxiliary functions a
n(x), b
n(x). The main result consists of the conclusion that under an appropriate choice of a
n(x), b
n(x), the operator \(\widetilde {P}_n: C[0,\infty )\to C[0,\infty )\) has two eigenfunctions exp(c
i
x) associated with the same unit eigenvalue. Here, c
1 < c
2 are real numbers. We establish direct estimates, including a quantitative asymptotic formula for the modified form of the operators. Finally, we represent the error graphically using the software Mathematica.