Для заданого $Q_S$ -зображення чисел $x ∈ [0;1]$, яке є узагальненням класичного трiйкового зображення, i визначається параметрами  $q_0,q_1,q_2,...q_{s-1}  (q_i>0, \sum_{i=0}^{s-1} q_i=1$ та наступною рiвнiстю

$x=β_{α_1(x)} + \sum_∞^{k=2} [β_{α_k(x)} \prod_{j =1}^{k-1} q_{a_j(x)}] ≡ \Delta_{a_1(x) a_2(x)...a_n(x)...}^{Q_S}$,

де $a_k(x) ∈ A_S ≡$ {$0,1,2,...,s-1$}, $β_0=0, β_i=\sum_{j=0}^{i-1} q_j$, вивчаються функцiї

$ω_n(\Delta_{a_1 a_2...a_n...}^{Q_S}) = \Delta_{a_1 a_2...a_{n-2} a_{n-1} a_{n+1} a_{n+2}...}^{Q_S}$

та

$f_{ni}(\Delta_{a_1 a_2...a_n...}^{Q_S}) = \Delta_{a_1 a_2...a_{n-1} i a_n a_{n+1} ...}^{Q_S}$,де $n,i ∈ N$.

Доведено, що всi функцiї є кусково-неперервними та мають скiнченну кiлькiсть точок розриву першого роду, знайдено їх аналiтичний вираз. Розлянуто застосування у метричних задачах.

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