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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.Book Part Recent Trends on Ulam–Hyers Stability Results of Fixed Point Problems(World Scientific Publishing Co., 2025) Cvetković, M.; Karapınar, E.; Ye Silkaya, S.S.Fixed point theorems have been extensively used in recent years to prove the Ulam–Hyers stability results of functional equations. In this chapter, we collect novel Ulam–Hyers stability results obtained by using well-known fixed point theorems in the setting of a complete metric space. We focus on several types of functional equations and inclusions along with some applications on the stability of the specific integral and differential equation. © 2026 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
