The achievement set of generalized multigeometric sequences
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913317690277888 |
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| author | Karvatskyi, Dmytro Murillo, Aniceto Viruel, Antonio |
| author_facet | Karvatskyi, Dmytro Murillo, Aniceto Viruel, Antonio |
| contents | We study the topology of all possible subsums of the generalized multigeometric series $k_1f(x)+k_2f(x)+\dots+k_mf(x)+\dots + k_1f(x^n)+\dots+k_mf(x^n)+\dots,$ where $k_1, k_2, \dots, k_m$ are fixed positive real numbers and $f$ runs along a certain class of non-negative functions on the unit interval. We detect particular regions of this interval for which this achievement set is, respectively, a compact interval, a Cantor set and a Cantorval. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_11388 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The achievement set of generalized multigeometric sequences Karvatskyi, Dmytro Murillo, Aniceto Viruel, Antonio Classical Analysis and ODEs General Topology 40A05, 11B05, 28A80 We study the topology of all possible subsums of the generalized multigeometric series $k_1f(x)+k_2f(x)+\dots+k_mf(x)+\dots + k_1f(x^n)+\dots+k_mf(x^n)+\dots,$ where $k_1, k_2, \dots, k_m$ are fixed positive real numbers and $f$ runs along a certain class of non-negative functions on the unit interval. We detect particular regions of this interval for which this achievement set is, respectively, a compact interval, a Cantor set and a Cantorval. |
| title | The achievement set of generalized multigeometric sequences |
| topic | Classical Analysis and ODEs General Topology 40A05, 11B05, 28A80 |
| url | https://arxiv.org/abs/2309.11388 |