  In this paper, we are concerned with the following viscoelastic wave equation
\begin{equation*} \label{1} u_{tt}-\nabla u +\int_0^t g_1 (t-s)~ div(a_1(x)
\nabla u(s))~ ds + \int_0^{+ \infty} g_2 (s)~ div(a_2(x) \nabla u(t-s)) ~ds =
0, \end{equation*} in a bounded domain $\Omega$. Under suitable conditions on
$a_1$ and $a_2$ and for a wide class of relaxation functions $g_1$ and $g_2$.
We establish a general decay result. The proof is based on the multiplier
method and makes use of convex functions and some inequalities. More
specifically, we remove the constraint imposed on the boundedness condition on
the initial data $\nabla u_{0}$. This study generalizes and improves previous
literature outcomes.
