Abstract. 

In this paper we introduce a new orbit-based contractive framework in the setting of G-metric spaces, called (m, α) G-path-averaged (G-PA) contractions with m ≥2. This notion extends Fabiano’s path-averaged contractions to the triadic geometry of Mustafa–Sims G-metrics and is designed to avoid collapse to pointwise contractility. For a G-continuous self-map on a complete G-metric space, we establish existence and uniqueness of a fixed point and prove that the Picard iteration converges to it in the sense of G-convergence. Moreover, we derive explicit quantitative estimates, including a posteriori and a priori geometric error bounds for the iterates. We also relate the new class to the induced metric dG, showing that every G-PA contraction yields a path-averaged contraction on (X, dG), and we provide examples demonstrating that the G-PA class can be strictly larger than the Banach-type contraction class. Finally, we obtain multi-step (t-point) fixed point and convergence results by embedding the recursion into a shift map on the product space (Xt , Gt) and applying the single-valued theory.