Path Averaged Polynomial Contractions: A New Generalization of Polynomial Contractions, Path-Averaged Contractions, and Banach Contractions

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 [6] in suprametric spaces. In this paper, we combine both notions to introduce path-averaged polynomial contractions, as a generalization of polynomial contractions, path-averaged contractions, and Banach contractions. We obtain a fixed point theorem for such contractions in the setting of complete metric spaces under continuity and boundedness assumptions on the coefficient functions. We give an example showing path-averaged polynomial contractions are not Banach contractions.