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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: 3Citation - Scopus: 6Fixed Points of Α-Admissible Meir-Keeler Contraction Mappings on Quasi-Metric Spaces(Springer international Publishing Ag, 2015) Alsulami, Hamed H.; Gulyaz, Selma; Erhan, Inci M.We introduce alpha-admissible Meir-Keller and generalized alpha-admissible Meir-Keller contractions on quasi-metric spaces and discuss the existence of fixed points of such contractions. We apply our results to G-metric spaces and express some fixed point theorems in G-metric spaces as consequences of the results in quasi-metric spaces.Article Citation - WoS: 40Citation - Scopus: 50Fixed Points of (ψ, Φ) Contractions on Rectangular Metric Spaces(Springer international Publishing Ag, 2012) Erhan, Inci M.; Karapinar, Erdal; Sekulic, TanjaExistence and uniqueness of fixed points of a general class of (psi, phi) contractive mappings on complete rectangular metric spaces are discussed. One of the theorems is a generalization of a fixed point theorem recently introduced by Lakzian and Samet. Fixed points of (psi, phi) contractions under conditions involving rational expressions are also investigated. Several particular cases and applications as well as an illustrative example are given.Article Citation - WoS: 1Citation - Scopus: 2Common Fixed Point of Multifunctions on Partial Metric Spaces(Springer international Publishing Ag, 2015) Aleomraninejad, S. Mohammad Ali; Erhan, Inci M.; Kutbi, Marwan A.; Shokouhnia, MasoumehIn this paper, some multifunctions on partial metric space are defined and common fixed points of such multifunctions are discussed. The results presented in the paper generalize some of the existing results in the literature. Several conclusions of the main results are given.Article Citation - WoS: 6Citation - Scopus: 5A Note on 'coupled Fixed Point Theorems for Mixed g-monotone Mappings in Partially Ordered Metric Spaces'(Springer international Publishing Ag, 2014) Bilgili, Nurcan; Erhan, Inci M.; Karapinar, Erdal; Turkoglu, DuranRecently, some (common) coupled fixed theorems in various abstract spaces have appeared as a generalization of existing (usual) fixed point results. Unexpectedly, we noticed that most of such (common) coupled fixed theorems are either weaker or equivalent to existing fixed point results in the literature. In particular, we prove that the very recent paper of Turkoglu and Sangurlu 'Coupled fixed point theorems for mixed g-monotone mappings in partially ordered metric spaces [Fixed Point Theory and Applications 2013, 2013:348]' can be considered as a consequence of the existing fixed point theorems on the topic in the literature. Furthermore, we give an example to illustrate that the main results of Turkoglu and Sangurlu (Fixed Point Theory Appl. 2013:348, 2013) has limited applicability compared to the mentioned existing fixed point result.Article Citation - WoS: 13Citation - Scopus: 12Common Fixed Point Theorems of Integral Type Contraction on Metric Spaces and Its Applications To System of Functional Equations(Springer international Publishing Ag, 2015) Sarwar, Muhammad; Zada, Mian Bahadur; Erhan, Inci M.In this article, using the common (CLR) property, common fixed point results for two pairs of weakly compatible mappings satisfying contractive condition of integral type on metric spaces are established. Furthermore, the existence and uniqueness of common solution for system of functional equations arising in dynamic programming are discussed as an application of a common fixed point theorem presented in this paper.Article Citation - WoS: 3Citation - Scopus: 5A Fixed Point Theorem for Meir-Keeler Type Contraction Via Gupta-Saxena Expression(Springer international Publishing Ag, 2015) Redjel, Najeh; Dehici, Abdelkader; Erhan, Inci M.In this paper, following the idea of Samet et al. (J. Nonlinear. Sci. Appl. 6: 162-169, 2013), we establish a new fixed point theorem for a Meir-Keeler type contraction via Gupta-Saxena rational expression which enables us to extend and generalize their main result (Gupta and Saxena in Math. Stud. 52: 156-158, 1984). As an application we derive some fixed points of mappings of integral type.Article Citation - WoS: 24Citation - Scopus: 5Remarks on 'Coupled coincidence point results for a generalized compatible pair with applications'(Springer international Publishing Ag, 2014) Erhan, Inci M.; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Shahzad, NaseerVery recently, Hussain et al. (Fixed Point Theory Appl. 2014:62, 2014) announced the existence and uniqueness of some coupled coincidence point. In this short note we remark that the announced results can be derived from the coincidence point results in the literature.Article Citation - WoS: 14Citation - Scopus: 18Some fixed point theorems for (α, ψ)-rational type contractive mappings(Springer international Publishing Ag, 2015) Alsulami, Hamed H.; Chandok, Sumit; Taoudi, Mohamed-Aziz; Erhan, Inci M.In this paper, we introduce the concept of (alpha, psi)-rational type contractive mappings and provide sufficient conditions for the existence and uniqueness of a fixed point for such class of generalized nonlinear contractive mappings in the setting of generalized metric spaces. We also deduce several interesting corollaries.
