A Gauss-Kuzmin-type problem for a family of continued fraction expansions
The aim of the present paper is to find out a version of the well-known Gauss-Kuzmin type problem for a family of non-regular continued fraction expansions of any number in the unit interval \(I=[0,1]\) with digits which are differences of consecutive non-positive integer powers of any integer \(m\geq 2\) introduced by \textit{H.-C. Chan} [Fibonacci Q. 44, No. 1, 73--84 (2006; Zbl 1204.11032)] following the theory of random systems with complete connections by \textit{M. Iosifescu} and \textit{S. Grigorescu} [Dependence with complete connections and its applications. Cambridge (UK): Cambridge University Press (1990; Zbl 0749.60067); second printing slightly corrected (2009; Zbl 1154.60060)].
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