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Article Citation - WoS: 143Citation - Scopus: 141Coupled Fixed Point Results for (ψ, Φ)-Weakly Contractive Condition in Ordered Partial Metric Spaces(Pergamon-elsevier Science Ltd, 2011) Aydi, Hassen; Karapinar, Erdal; Shatanawi, WasfiIn this paper, we prove some coupled fixed point theorems involving a (psi, phi)-weakly contractive condition for mapping having the mixed monotone property in ordered partial metric spaces. These results are analogous to theorems of Van Luong and Xuan Thuan (2011) [10] on the class of ordered partial metric spaces. Also, an application is given to support our results. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 40Citation - Scopus: 36Common Fixed Points for Generalized -Implicit Contractions in Partial Metric Spaces: Consequences and Application(Springer-verlag Italia Srl, 2015) Aydi, Hassen; Jellali, Manel; Karapinar, ErdalIn this paper, we introduce the concept of generalized -admissible pair of mappings generalizing the definition of -admissible mappings presented by Samet et al. (Nonlinear Anal 75:2154-2165, 2012). Based on above, we define generalized -implicit contractions in the setting of partial metric spaces and we provide some common fixed point results for such contractions. We also derive some consequences and corollaries from our obtained results. An application and some examples are presented making effective the new concepts and results.Article Citation - WoS: 63Citation - Scopus: 78Fixed Points for Generalized (α, Ψ)-Contractions on Generalized Metric Spaces(Springeropen, 2014) Aydi, Hassen; Karapinar, Erdal; Samet, BessemIn this paper, we introduce some generalized (alpha, psi)-contractive mappings in the setting of generalized metric spaces and, based on the very recent paper (Kirk and Shahzad in Fixed Point Theory Appl. 2013:129, 2013), we omit the Hausdorff hypothesis to prove some fixed point results involving such mappings. Some consequences on existing fixed point theorems are also derived.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: 172Citation - Scopus: 190Interpolative 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, 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: 27Citation - Scopus: 25A Discussion on Generalized Almost Contractions Via Rational Expressions in Partially Ordered Metric Spaces(Springeropen, 2014) Mustafa, Zead; Karapinar, Erdal; Aydi, HassenThe main purpose of this paper is to give some fixed point results for mappings involving generalized (phi, psi)-contractions in partially ordered metric spaces. Our results generalize, extend, and unify several well-known comparable results in the literature (Jaggi in Indian J. Pure Appl. Math. 8(2):223-230, 1977, Harjani et al. in Nonlinear Anal. 71:3403-3410, 2009, Luong and Thuan in Fixed Point Theory Appl. 2011:46, 2011). The presented results are supported by three illustrative examples.Article Citation - WoS: 20Citation - Scopus: 18MEIR-KEELER TYPE CONTRACTIONS FOR TRIPLED FIXED POINTS(Springer, 2012) Aydi, Hassen; Karapinar, Erdal; Vetro, CalogeroIn 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction.
