Asymptotic properties for a general class of Szasz-Mirakjan-Durrmeyer operators
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913442460336128 |
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| author | Abel, Ulrich Acu, Ana Maria Heilmann, Margareta Rasa, Ioan |
| author_facet | Abel, Ulrich Acu, Ana Maria Heilmann, Margareta Rasa, Ioan |
| contents | In this paper we introduce a general family of Szász--Mirakjan--Durrmeyer type operators depending on an integer parameter $j \in \mathbb{Z}$. They can be viewed as a generalization of the Szász--Mirakjan--Durrmeyer operators [9], Phillips operators [11] and corresponding Kantorovich modifications of higher order.
For $j\in {\mathbb{N}}$, these operators possess the exceptional property to preserve constants and the monomial $x^{j}$. It turns out, that an extension of this family covers certain well-known operators studied before, so that the outcoming results could be unified.
We present the complete asymptotic expansion for the sequence of these operators. All its coefficients are given in a concise form. In order to prove the expansions for the class of locally integrable functions of exponential growth on the positive half-axis, we derive a localization result which is interesting in itself. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16474 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic properties for a general class of Szasz-Mirakjan-Durrmeyer operators Abel, Ulrich Acu, Ana Maria Heilmann, Margareta Rasa, Ioan Classical Analysis and ODEs Numerical Analysis In this paper we introduce a general family of Szász--Mirakjan--Durrmeyer type operators depending on an integer parameter $j \in \mathbb{Z}$. They can be viewed as a generalization of the Szász--Mirakjan--Durrmeyer operators [9], Phillips operators [11] and corresponding Kantorovich modifications of higher order. For $j\in {\mathbb{N}}$, these operators possess the exceptional property to preserve constants and the monomial $x^{j}$. It turns out, that an extension of this family covers certain well-known operators studied before, so that the outcoming results could be unified. We present the complete asymptotic expansion for the sequence of these operators. All its coefficients are given in a concise form. In order to prove the expansions for the class of locally integrable functions of exponential growth on the positive half-axis, we derive a localization result which is interesting in itself. |
| title | Asymptotic properties for a general class of Szasz-Mirakjan-Durrmeyer operators |
| topic | Classical Analysis and ODEs Numerical Analysis |
| url | https://arxiv.org/abs/2407.16474 |