  Let $A$ be a Banach algebra with a non-empty character space. We say that a
bounded net $\{e_{\alpha}\}$ in $A$ is a bounded $\Delta$-weak approximate
identity for $A$ if, for each $a\in A$ and compact subset $K$ of $\Delta(A)$,
$||\widehat{e_{\alpha}a}-\widehat{a}||_{K}=\sup_{\phi\in
K}|\phi(e_{\alpha}a)-\phi(a)|\rightarrow 0$. For each $1<p<\infty$, we prove
that the Figa-Talamanca Herz algebra, $A_{p}(G)$ has a bounded $\Delta$-weak
approximate identity if and only if $G$ is an amenable group. Also we give a
sufficient condition for amenability of group $G$.
