On the Novelty of “Contracting Perimeters of Triangles in Metric Space”

Abstract

In this note, we investigate whether the newly introduced notion of “contracting perimeters of triangles” in the context of standard metric spaces is novel or equivalent to “a variant” of Banach contraction in the setting of G-metric spaces. By using the fact that G-metric spaces are equivalent to quasi-metric spaces, we reconsider our main question as whether the fixed-point theorems via “contracting perimeters of triangles” is equivalent to a fixed point of the same mapping in the context of quasi-metric spaces. © 2025, Erdal Karapinar. All rights reserved.