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Article Citation - WoS: 3Citation - Scopus: 7Some Almost Generalized (ψ, Φ)-Contractions in g-metric Spaces(Hindawi Ltd, 2013) Aydi, Hassen; Amor, Sana Hadj; Karapinar, Erdal; Hadj Amor, SanaIn this paper, we introduce some almost generalized (psi, phi)-contractions in the setting of G-metric spaces. We prove some fixed points results for such contractions. The presented theorems improve and extend some known results in the literature. An example is also presented.Article Citation - WoS: 11Citation - Scopus: 8Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized Meir-Keeler Type Contractions(Hindawi Ltd, 2012) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.We prove coupled coincidence point and coupled fixed point results of F : X x X -> X and g : X -> X involving Meir-Keeler type contractions on the class of partially ordered metric spaces. Our results generalize some recent results in the literature. Also, we give some illustrative examples and application.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: 25Citation - Scopus: 31Best proximity points and extension of Mizoguchi-Takahashi's fixed point theorems(Springer int Publ Ag, 2013) Kumam, Poom; Aydi, Hassen; Karapinar, Erdal; Sintunavarat, WutipholIn this paper, we introduce a multi-valued cyclic generalized contraction by extending the Mizoguchi and Takahashi's contraction for non-self mappings. We also establish a best proximity point for such type contraction mappings in the context of metric spaces. Later, we characterize this result to investigate the existence of best proximity point theorems in uniformly convex Banach spaces. We state some illustrative examples to support our main theorems. Our results extend, improve and enrich some celebrated results in the literature, such as Nadler's fixed point theorem, Mizoguchi and Takahashi's fixed point theorem.Article Citation - WoS: 49On Fixed Point Results for Α-Implicit Contractions in Quasi-Metric Spaces and Consequences(inst Mathematics & informatics, 2016) Aydi, Hassen; Jellali, Manel; Karapinar, ErdalIn this paper, we prove some fixed point results involving alpha-implicit contractions in quasi-metric spaces. Moreover, we provide some known results on G-metric spaces. An example and an application on a solution of a nonlinear integral equation are also presented.Article Citation - WoS: 21Citation - Scopus: 23Best Proximity Points of Generalized Almost Ψ-Geraghty Contractive Non-Self(Springer international Publishing Ag, 2014) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.; Salimi, PeymanIn this paper, we introduce the new notion of almost psi-Geraghty contractive mappings and investigate the existence of a best proximity point for such mappings in complete metric spaces via the weak P-property. We provide an example to validate our best proximity point theorem. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature.
