In a recent paper by M. Rathjen and the present author it has been shown that the statement "every normal function has a derivative" is equivalent to Π11-bar induction. The equivalence was proved over ACA0, for a suitable representation of normal functions in terms of dilators. In the present paper, we show that the statement "every normal function has at least one fixed point" is equivalent to Π11-induction along the natural numbers.