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