Abstract
AbstractWe study the topology of all possible subsums of the generalized multigeometric series$$k_1f(x)+k_2f(x)+\dots +k_mf(x)+\dots + k_1f(x^n)+\dots +k_mf(x^n)+\dots ,$$
k
1
f
(
x
)
+
k
2
f
(
x
)
+
⋯
+
k
m
f
(
x
)
+
⋯
+
k
1
f
(
x
n
)
+
⋯
+
k
m
f
(
x
n
)
+
⋯
,
where $$k_1, k_2, \dots , k_m$$
k
1
,
k
2
,
⋯
,
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.
Funder
Agencia Estatal de Investigación
Publisher
Springer Science and Business Media LLC
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