Box dimension of the graphs of the generalized Weierstrass-type functions

For a Lipschitz $ \mathbb{Z}- $periodic function \phi:\mathbb{R}\to \mathbb{R}^2 such that \mathbb{R}^2\setminus\{\phi(x):x\in\mathbb{R}\} is not connected, an integer b\ge 2 and \lambda\in (c/{b^{\frac12}},1) $, we prove the following for generalized Weierstrass-type W(x) = \sum\limits_{n 0}^{\infty}{{\lambda}^n\phi(b^nx)} $: box dimension of its graph equal to 3+2\log_b\lambda where c constant depending on \phi $.