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Article Citation - WoS: 6Citation - Scopus: 9On Interpolative Metric Spaces(Univ Nis, Fac Sci Math, 2024) Karapinar, ErdalThe purpose of this article is to expand the "open discussion" on the definition and necessity of the interpolation metric space and keep it on the agenda of researchers in nonlinear functional analysis. The secondary aim of this article is to indicate that the outcomes of this "open discussion" have the potential to stop the recent recession in the metric fixed point theory.Article Citation - Scopus: 2On the Novelty of “Contracting Perimeters of Triangles in Metric Space”(Erdal Karapinar, 2025) Karapınar, E.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.
