The Achievement Set of Generalized Multigeometric Sequences - Karvatskyi, Dmytro; Murillo-Mas, Aniceto; Viruel-Arbaizar, Antonio Ángel (Springer, 2024)
We study the topology of all possible subsums of the generalized multigeometric series where 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.
Keywords: Geometría; Subsums set; Cantor set; Achievement set; Cantorval; Multigeometric series