2026/04/05 by Clement Boateng Ampadu, Nicola Fabiano
#math.GM
The notion of polynomial contraction appeared in [2], whilst the notion of path-averaged contraction appeared in [3] for metric spaces, in [4,5] for b-metric spaces, , and in [6] for suprametric spaces. In this paper, we combine both notions to introduce path-averaged polynomial contractions, as a generaliation of polynomial contractions, path-averaged contractions, and Banach contractions.We obtain a fixed point theorem for such contractions in the setting of metric spaces.We give an example showing path-averaged polynomial contractions are not Banach contractions