2025/10/01 by Nicola Fabiano, Fabiano, Nicola · 1 citation
Economics, Econometrics and Finance · #47H10 47H10 #54E50 #FOS: Mathematics #Functional Analysis (math.FA) #Game Theory and Voting Systems
paper · pdf · doi:10.48550/arxiv.2510.01496
openalex publication_date 2025/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a novel class of self-mappings on metric spaces, called PA-contractions (Path-Averaged Contractions), defined by an averaging condition over iterated distances. We prove that every continuous PA-contraction on a complete metric space has a unique fixed point, and the Picard iterates converge to it. This condition strictly generalizes the classical Banach contraction principle. We provide examples showing that PA-contractions are independent of F-contractions, Kannan, Chatterjea, and Ćirić contractions. A comparison table highlights the distinctions. The PA-condition captures long-term contractive behavior even when pointwise contraction fails.