  We investigate some Weihrauch problems between $\mathsf{ATR}_2$ and
$\mathsf{C}_{\omega^\omega}$ . We show that the fixed point theorem for
monotone operators on the Cantor space (a weaker version of the Knaster-Tarski
theorem) is not Weihrauch reducible to $\mathsf{ATR}_2$. Furthermore, we
introduce the $\omega$-model reflection $\mathsf{ATR}_2^{\mathrm{rfn}}$ of
$\mathsf{ATR} $ and show that it is an upper bound for problems provable from
the axiomatic system $\mathrm{ATR}_0$ which are of the form $\forall
X(\theta(X) \to \exists Y \eta(X, Y ))$ with arithmetical formulas $\theta,
\eta$. We also show that Weihrauch degrees of relativized least fixed point
theorem for monotone operators on the Cantor space forms a linear hierarchy
between $\mathsf{ATR}^{\mathrm{rfn}}$ and $\mathsf{C}_{\omega^\omega} $.
