A Short Note on $P$-Contractive and Picard Operators

Altun and Hancer \cite{AltunHancer2019} proved that every continuous $P$-contractive self-map of compact metric space is an almost Picard operator, and asked whether it must in fact be a Picard operator. We give an affirmative answer. The proof follows by combining the existing results with a final compactness argument.