Kernels for composition of positive linear operators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918076144943104 |
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| author | Abel, Ulrich Acu, Ana Maria Heilmann, Margareta Raşa, Ioan |
| author_facet | Abel, Ulrich Acu, Ana Maria Heilmann, Margareta Raşa, Ioan |
| contents | This paper investigates the composition of Bernstein--Durrmeyer operators and Szász--Mirakjan--Durrmeyer operators, focusing on the structure and properties of the associated kernel functions. In the case of the Bernstein--Durrmeyer operators, we establish new identities for the kernel arising from the composition of two and three operators, from which the commutativity of these operators follows naturally. Building on the eigenstructure of the Bernstein--Durrmeyer operator $M_n$, we obtain a representation of the iterate $M_n^r$ as a linear combination of the operators $M_k$, for $k=0,1,\dots,n$. We also address the composition of Szász--Mirakjan--Durrmeyer operators and revisit a known result giving an elementary proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kernels for composition of positive linear operators Abel, Ulrich Acu, Ana Maria Heilmann, Margareta Raşa, Ioan Classical Analysis and ODEs 41A36 This paper investigates the composition of Bernstein--Durrmeyer operators and Szász--Mirakjan--Durrmeyer operators, focusing on the structure and properties of the associated kernel functions. In the case of the Bernstein--Durrmeyer operators, we establish new identities for the kernel arising from the composition of two and three operators, from which the commutativity of these operators follows naturally. Building on the eigenstructure of the Bernstein--Durrmeyer operator $M_n$, we obtain a representation of the iterate $M_n^r$ as a linear combination of the operators $M_k$, for $k=0,1,\dots,n$. We also address the composition of Szász--Mirakjan--Durrmeyer operators and revisit a known result giving an elementary proof. |
| title | Kernels for composition of positive linear operators |
| topic | Classical Analysis and ODEs 41A36 |
| url | https://arxiv.org/abs/2506.23579 |