The FixedPoint command applies a function to an expression until the result no longer changes.

$\mathrm{with}\left(\mathrm{MmaTranslator}\left[\mathrm{Mma}\right]\right)\:$

$\mathrm{FixedPoint}\left(\cos \,0.5\right)$

$0.7390851332$

$\mathrm{with}\left(\mathrm{MmaTranslator}\right)\:$

$\mathrm{FromMma}\left(\mathrm{`FixedPoint[Cos,\; 0.5]`}\,\mathrm{evaluate}\right)$

$0.7390851332$