Box dimension of generalized affine fractal interpolation functions

Let $f$ be a generalized affine fractal interpolation function with vertical scaling function $S$. In this paper, we study ${\dim }_B\mathrm{\Gamma }f$, the box dimension of the graph of $f$, under the assumption that $S$ is a Lipschtz function. By introducing vertical scaling matrices, we estimate the upper bound and the lower bound of oscillations of $f$. As a result, we obtain explicit formula of ${\dim }_B\mathrm{\Gamma }f$ under certain constraint conditions.