Zero product determined of abstract Segal algebras

At the present article, we investigate the notion of zero product determined for category of abstract Segal algebras. Indeed, where $\mathfrak{X}$ is an abstract segal algebra with respect to $\mathfrak{A},$ we prove that under some conditions this notion inherits from $\mathfrak{X}$ to $\mathfrak{A}.$ Applying these results, we obtain some sufficient conditions in which the Fourier algebra $A(\mathfrak{G})$ is zero product determined, when $\mathfrak{G}$ is a locally compact group.