I have seen these 2 fixed point theorem and I think the condition of Leray Schauder fixed point theorem is very strong and we require to consider the fixed point of $u=\sigma Tu$ $\forall \sigma \in[0,1]$.

And I think the result of schauder fixed point theorem is stronger than that of Leray Schauder , Do I have any misunderstanding about these 2 theorem?

Thank you