Power boundedness in Fourier and Fourier-Stieltjes algebra of an ultraspherical hypergroup

Let $H$ be an ultraspherical hypergroup associated with a locally compact group $G$ and a spherical projector $\pi$ and let $A(H)$ and $B(H)$ denote the Fourier and Fourier-Stieltjes algebras, respectively, associated with $H\mathrm{.}$ In this note, we study power boundedness and Cesàro boundedness in $B(H)$. We also characterize the power bounded property for both $A(H)$ and $B(H)\mathrm{.}$