Two new examples of Banach spaces with a plastic unit ball

We prove that Banach spaces ${\mathrm{\ell }}_1{\oplus }_2\mathbb{R}$ and $X\oplus_\infty Y$,withstrictlyconvex$X$and$Y$, have plastic unit balls (we call a metric space plastic if every non-expansive bijection from this space onto itself is an isometry).