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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.Article Mild Solutions for Neutral Conformable Fractional Order Functional Evolution Equations Using Meir-Keeler Type Fixed Point Theorem(Politechnica University of Bucharest, 2025) Berrighi, F.; Medjadj, I.; Karapınar, E.Our mission is to demonstrate the existence, uniqueness, attractiveness, and controllability of mild solutions to neutral conformable fractional-order functional evolution equations, specifically of order between 1 and 2. These intriguing equations encompass finite delay, all while adhering to local conditions within a separable Banach space. By invoking Meir-Keeler’s fixed-point Theorem and enhancing it with measures of noncompactness, we establish the existence of these solutions. To highlight the potency of our approach, we present a captivating example. © 2025, Politechnica University of Bucharest. 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.Article On the Metrizability of Suprametric Space(Sciendo, 2025) Karapınar, E.; Cvetković, M.The question of metrizability of suprametric space is answered positively. The observed metric coincides with a suprametric in a way that convergence and continuity are preserved between suprametric space and associated metric space along with the propery of a Cauchy sequence. Consequently, a suprametric space is complete if and only if associated metric space is complete. Fixed point theorems in suprametric space are obtained as a corollary of well-known fixed point results. © 2025 Erdal Karaplnar et al.
