A Generalization of the Gauss-Kuzmin-Wirsing constant

TL;DR

This paper extends Wirsing's results on the Gauss transformation to a broader class of transformations parameterized by positive integers, providing estimates for the associated generalized Gauss-Kuzmin-Wirsing constants.

Contribution

It introduces a generalization of the Gauss-Kuzmin-Wirsing constant for transformations $T_p(x)=\{p/x\}$, expanding the theoretical understanding of these dynamical systems.

Findings

Derived estimates for the generalized Gauss-Kuzmin-Wirsing constant.

Extended the applicability of Gauss transformation analysis to new classes.

Provided theoretical bounds for convergence rates in generalized settings.

Abstract

We generalize the result of Wirsing on Gauss transformation to the generalized tranformation $T_p(x)=\{\cfrac{p}{x}\}$ for any positive integer $p$. We give an estimate for the generalized Gauss-Kuzmin-Wirsing constant.