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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: 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.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: 88Citation - Scopus: 97Modified f-contractions Via α-admissible Mappings and Application To Integral Equations(Univ Nis, Fac Sci Math, 2017) Aydi, Hassen; Karapinar, Erdal; Yazidi, HabibIn this paper, we introduce the concept of a modified F-contraction via alpha-admissible mappings and propose some theorems that guarantee the existence and uniqueness of fixed point for such mappings in the frame of complete metric spaces. We also provide some illustrative examples. Moreover, we consider an application solving an integral equation.Article Citation - WoS: 78Citation - Scopus: 63Discussion on Some Coupled Fixed Point Theorems(Springer international Publishing Ag, 2013) Samet, Bessem; Karapinar, Erdal; Aydi, Hassen; Rajic, Vesna CojbasicIn this paper, we show that, unexpectedly, most of the coupled fixed point theorems (on ordered metric spaces) are in fact immediate consequences of well-known fixed point theorems in the literature. MSC: 47H10, 54H25.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: 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: 25Citation - Scopus: 32Remarks on Some Recent Fixed Point Theorems(Springer international Publishing Ag, 2012) Aydi, Hassen; Karapinar, Erdal; Samet, BessemThe purpose of this article is to show that some recent fixed point theorems are particular results of previous existing theorems in the literature. Mathematics Subject Classification 2000: 54H25; 47H10.Article Citation - WoS: 103Citation - Scopus: 108On Generalized Α - Ψ-Geraghty Contractions on b-metric Spaces(Walter de Gruyter Gmbh, 2020) Afshari, Hojjat; Aydi, Hassen; Karapinar, ErdalIn this paper, we consider generalized alpha - psi-Geraghty contractive type mappings and investigate the existence and uniqueness of a fixed point for mappings involving such contractions. In particular, we extend, improve and generalize some earlier results in the literature on this topic. An application concerning the existence of an integral equation is also considered to illustrate the novelty of the main result.Article Citation - WoS: 15FIXED POINT RESULTS FOR GENERALIZED α-ψ-CONTRACTIONS IN METRIC-LIKE SPACES AND APPLICATIONS(Texas State Univ, 2015) Aydi, Hassen; Karapinar, ErdalIn this article, we introduce the concept of generalized alpha-psi-contraction in the context of metric-like spaces and establish some related fixed point theorems. As consequences, we obtain some known fixed point results in the literature. Some examples and an application on two-point boundary value problems for second order differential equation are also considered.
