Let H be an ultraspherical hypergroup and let $A(H)$ be the Fourier algebra associated with $H.$ In this paper, we study the dual and the double dual of $A(H).$ We prove among other things that the subspace of all uniformly continuous functionals on $A(H)$ forms a $C^*$-algebra. We also prove that the double dual $A(H)^{\ast \ast }$ is neither commutative nor semisimple with respect to the Arens product, unless the underlying hypergroup H is finite. Finally, we study the unit elements of $A(H)^{\ast \ast }.$

Let $G$ be a locally compact group. Let ${{A}_{M}}\left( G \right)\,\left( {{A}_{0}}\left( G \right) \right)$ denote the closure of $A\left( G \right)$, the Fourier algebra of $G$ in the space of bounded (completely bounded) multipliers of $A\left( G \right)$. We call a locally compact group $\text{M}$-weakly amenable if ${{A}_{M}}\left( G \right) $ has a bounded approximate identity. We will show that when $G$ is $\text{M}$-weakly amenable, the algebras ${{A}_{M}}\left( G \right) $ and ${{A}_{0}}\left( G \right)$ have properties that are characteristic of the Fourier algebra of an amenable group. Along the way we show that the sets of topologically invariant means associated with these algebras have the same cardinality as those of the Fourier algebra.