LIMIT BEHAVIOR OF THE QUASI-LINEAR DISCRETE FUNCTIONS

Abstract

In this paper, we focus on the limit behavior of the quasi-linear functions, including some [Formula: see text]-regular sequences. The limit behavior of the quasi-linear functions is presented through their induced limit functions. We show that these limit functions are continuous and self-similar. Moreover, the graphs of the limit functions are fractal curves. We give an estimation of the upper and lower box dimensions of the graphs of the limit functions. Under certain condition, the exact value of the box dimensions of the graphs of the limit functions is obtained.