Abstract Let \aₙ (x) \₍ ₁ be the sequence of digits of x (0, 1) in an infinite iterated function system with polynomial decay of the derivative. We first study the multifractal spectrum of the convergence exponent, defined by the sequence of digits \aₙ (x) \₍ ₁ and the weighted products of distinct digits with finite numbers, and then calculate the Hausdorff dimensions of the intersections of sets defined by the convergence exponent of the weighted product of distinct digits with finite numbers and sets of points whose digits are nondecreasing in such iterated function systems.
Song et al. (2026) studied this question.