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Article Citation - WoS: 12Citation - Scopus: 18On the existence of fixed points that belong to the zero set of a certain function(Springer international Publishing Ag, 2015) Karapinar, Erdal; O'Regan, Donal; Samet, BessemLet T : X -> X be a given operator and F-T be the set of its fixed points. For a certain function phi : X -> [0,infinity), we say that F-T is phi-admissible if F-T is nonempty and F-T subset of Z(phi), where Z(phi) is the zero set of phi. In this paper, we study the phi-admissibility of a new class of operators. As applications, we establish a new homotopy result and we obtain a partial metric version of the Boyd-Wong fixed point theorem.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: 9Citation - Scopus: 9Fixed Point Theorems for Various Classes of Cyclic Mappings(Hindawi Ltd, 2012) Aydi, Hassen; Karapinar, Erdal; Samet, BessemWe introduce new classes of cyclic mappings and we study the existence and uniqueness of fixed points for such mappings. The presented theorems generalize and improve several existing results in the literature.Article Citation - WoS: 61Best Proximity Points for Generalized α-ψ-Proximal Contractive Type Mappings(Hindawi Ltd, 2013) Jleli, Mohamed; Karapinar, Erdal; Samet, BessemWe introduce a new class of non-self-contractive mappings. For such mappings, we study the existence and uniqueness of best proximity points. Several applications and interesting consequences of our obtained results are derived.Article Citation - WoS: 97Citation - Scopus: 147Further Generalizations of the Banach Contraction Principle(Springeropen, 2014) Jleli, Mohamed; Karapinar, Erdal; Samet, BessemWe establish a new fixed point theorem in the setting of Branciari metric spaces. The obtained result is an extension of the recent fixed point theorem established in Jleli and Samet (J. Inequal. Appl. 2014: 38, 2014).Article Citation - WoS: 7Positive Solutions for Multipoint Boundary Value Problems for Singular Fractional Differential Equations(Hindawi Ltd, 2014) Jleli, Mohamed; Karapinar, Erdal; Samet, BessemA class of nonlinear multipoint boundary value problems for singular fractional differential equations is considered. By means of a coupled fixed point theorem on ordered sets, some results on the existence and uniqueness of positive solutions are obtained.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: 15Citation - Scopus: 15A Note on 'ψ-geraghty Type Contractions'(Springer international Publishing Ag, 2014) Karapinar, Erdal; Samet, BessemVery recently, the notion of a psi-Geraghty type contraction was defined by Gordji et al. (Fixed Point Theory and Applications 2012: 74, 2012). In this short note, we realize that the main result via psi-Geraghty type contraction is equivalent to an existing related result in the literature. Consequently, all results inspired by the paper of Gordji et al. in (Fixed Point Theory and Applications 2012:74, 2012) can be derived in the same way.Article Citation - WoS: 1Citation - Scopus: 5A Note on Recent Fixed Point Results Involving g-quasicontractive Type Mappings in Partially Ordered Metric Spaces(Springer international Publishing Ag, 2014) Karapinar, Erdal; Samet, BessemIn this note, we establish the equivalence between recent fixed point theorems involving quasicontractive type mappings in metric spaces endowed with a partial order.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.
