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arXiv · 2309.11388

The achievement set of generalized multigeometric sequences

Dmytro Karvatskyi·Aniceto Murillo·Antonio Viruel
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Abstract

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.

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Dmytro Karvatskyi, Aniceto Murillo, Antonio Viruel. 2023-09-20. The achievement set of generalized multigeometric sequences. https://doi.org/10.1007/s00025-024-02158-8

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