On the Notion of a Function of Bounded Variation and of Riemann-Stieltjes Integral with Strong Partitions on Hyperbolic Intervals

In this paper we provided a classification for partitions of intervals on the hyperbolic plane. Given a partition, to be named strong, we define a notion of a hyperbolic-valued functions of bounded variation and a kind of Riemann-Stieltjes integral. A condition relating to both concepts appears to be natural for the existence of the integral, as it occurs in real analysis.