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A Wirsing-type approach to some continued fraction expansion. (English) Zbl 1081.11056
H.-C. Chan [Int. J. Math. Math. Sci. 2004, No. 20, 1067–1076 (2004; Zbl 1122.11046)] introduced a continued fraction expansion different from the regular continued fraction expansion, gave a solution to its Gauss-Kuzmin-Lévy problem, and showed a convergence rate. In this paper the author gives a better estimation of its convergence rate by using an approach seen in [Acta Arith. 24, 507–528 (1974; Zbl 0283.10032)]. The author’s strategy is to derive the Perron-Frobenius operator of the associated transformation under its invariant measure. Then the author obtains upper and lower bounds of the convergence rate, providing a near-optimal solution to the Gauss-Kuzmin-Lévy problem.

MSC:
11K50 Metric theory of continued fractions
37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)
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