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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. 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