There is R. Cauty paper from 2012 titled 'Un theoreme de Lefschetz-Hopf pour les fonctions a iterees compactes' which from what I heard was reviewed to establish a correct proof of Schauder's conjecture ( or rather a generalization for iterates of f ), and will appear in an international journal.
Edit: published: R. Cauty, J. Reine Angew. Math. 729 (2017), 1–27 DOI link
