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Article Citation - WoS: 11Citation - Scopus: 12Some Fixed Point Results on Interpolative Metric Spaces(Pergamon-elsevier Science Ltd, 2025) Karapinar, Erdal; Agarwal, Ravi P.This paper aims to introduce some basic fixed point theorems on interpolative metric space that is a natural extension of standard metric space.Article Citation - WoS: 25Citation - Scopus: 27A Generalization for the Best Proximity Point of Geraghty-Contractions(Springeropen, 2013) Bilgili, Nurcan; Karapinar, Erdal; Sadarangani, KishinIn this paper, we introduce the notion of Geraghty-contractions and consider the related best proximity point in the context of a metric space. We state an example to illustrate our result.Article Citation - WoS: 29Citation - Scopus: 36Fixed Point Results on a Class of Generalized Metric Spaces(Springer Heidelberg, 2012) Aydi, Hassen; Karapinar, Erdal; Lakzian, HosseinBrianciari ('A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces,' Publ. Math. Debrecen 57 (2000) 31-37) initiated the notion of the generalized metric space as a generalization of a metric space in such a way that the triangle inequality is replaced by the 'quadrilateral inequality,' d(x, y) <= d(x, a) + d(a, b) + d(b, y) for all pairwise distinct points x, y, a, and b of X. In this paper, we establish a fixed point result for weak contractive mappings T : X -> X in complete Hausdorff generalized metric spaces. The obtained result is an extension and a generalization of many existing results in the literature.Article Citation - WoS: 13Citation - Scopus: 16A Remark on "existence and Uniqueness for a Neutral Differential Problem With Unbounded Delay Via Fixed Point Results F-Metric Spaces"(Springer-verlag Italia Srl, 2019) Aydi, Hassen; Karapinar, Erdal; Mitrovic, Zoran D.; Rashid, TawseefVery recently, Hussain and Kanwal (Trans A Razmadze Math Inst 172(3): 481-490, 2018) proved some (coupled) fixed point results in this setting for a -.-contractive mappings on the setting of F-metric spaces that was initiated by Jleli and Samet (Fixed Point Theory Appl 2018: 128, 2018). In this note, we underline that the proof of Hussain and Kanwal (Trans A Razmadze Math Inst 172(3): 481-490, 2018) has a gap. We provide two examples to illustrate our observation. We also correct the proof and improved the result by replacing a-admissibility by orbital a-admissibility.Article Citation - WoS: 176Citation - Scopus: 196Interpolative Reich-Rus Type Contractions on Partial Metric Spaces(Mdpi, 2018) Karapinar, Erdal; Agarwal, Ravi; Aydi, HassenBy giving a counter-example, we point out a gap in the paper by Karapinar (Adv. Theory Nonlinear Anal. Its Appl. 2018, 2, 85-87) where the given fixed point may be not unique and we present the corrected version. We also state the celebrated fixed point theorem of Reich-Rus-Ciric in the framework of complete partial metric spaces, by taking the interpolation theory into account. Some examples are provided where the main result in papers by Reich (Can. Math. Bull. 1971, 14, 121-124; Boll. Unione Mat. Ital. 1972, 4, 26-42 and Boll. Unione Mat. Ital. 1971, 4, 1-11.) is not applicable.Article Citation - WoS: 27Citation - Scopus: 28Generalized Meir-Keeler Type Contractions on g-metric Spaces(Elsevier Science inc, 2013) Mustafa, Zead; Aydi, Hassen; Karapinar, ErdalIn this manuscript, we introduce generalized Meir-Keeler type contractions over G-metric spaces. Moreover, we show that every orbitally continuous generalized Meir-Keeler type contraction has a unique fixed point on complete G-metric spaces. We illustrate our results by some given examples. (C) 2013 Elsevier Inc. All rights reserved.Article Citation - WoS: 82Citation - Scopus: 87On Common Fixed Points in g-metric Spaces Using (e.a) Property(Pergamon-elsevier Science Ltd, 2012) Mustafa, Zead; Aydi, Hassen; Karapinar, Erdal; Karapnar, ErdalIn this paper, we introduce some new types of pairs of mappings (f, g) on G-metric spaces called G-weakly commuting of type G(f) and G-R-weakly commuting of type G(f). We obtain also several common fixed point results by using the (E.A) property. (c) 2012 Elsevier Ltd. All rights reserved.Article Citation - WoS: 178Citation - Scopus: 184Couple fixed point theorems for nonlinear contractions in cone metric spaces(Pergamon-elsevier Science Ltd, 2010) Karapinar, ErdalThe notion of coupled fixed point is introduced by Bhaskar and Lakshmikantham (2006) in [13]. In this manuscript, some results of Lakshmikantham and Ciric (2009) in [5] are extended to the class of cone metric spaces. (C) 2010 Elsevier Ltd. All rights reserved.Article Fixed Point Results on Perturbed B-Metric Space(Univ Belgrade, Fac Electrical Engineering, 2025) Karapinar, ErdalIn this paper, we introduce the notion of perturbed b-metric spaces and consider some basic topological notions on this new abstract structure. In addition, we shall discuss the existing and uniqueness of a fixed point in the setting of perturbed b-metric spaces.Article Citation - WoS: 4Citation - Scopus: 3On Orlicz-Power Series Spaces(Springer Basel Ag, 2010) Karapinar, Erdal; Zakharyuta, VyacheslavIn this manuscript, we investigate the isomorphisms of Orlicz-Kothe sequence spaces and quasidiagonal isomorphisms of Cartesian products of Orlicz-power series spaces.
