Browsing by Author "Samet, Bessem"
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Article Citation Count: 14A Best Proximity Point Result in Modular Spaces with the Fatou Property(Hindawi Ltd, 2013) Karapınar, Erdal; Karapinar, Erdal; Samet, Bessem; MathematicsConsider a nonself-mapping T: A -> B, where (A, B) is a pair of nonempty subsets of a modular space. X-rho. A best proximity point of T is a point z is an element of A satisfying the condition: rho(z - Tz) = inf {rho(x-y) : (x,y) is an element of A x B}. In this paper, we introduce the class of proximal quasicontraction nonself-mappings in modular spaces with the Fatou property. For such mappings, we provide sufficient conditions assuring the existence and uniqueness of best proximity points.Article Citation Count: 9Best Proximity Point Results for Mk-Proximal Contractions(Hindawi Publishing Corporation, 2012) Jleli, Mohamed; Karapınar, Erdal; Karapinar, Erdal; Samet, Bessem; MathematicsLet A and B be nonempty subsets of a metric space with the distance function d, and T : A -> B is a given non-self-mapping. The purpose of this paper is to solve the nonlinear programming problem that consists in minimizing the real-valued function x bar right arrow. d (x, Tx), where T belongs to a new class of contractive mappings. We provide also an iterative algorithm to find a solution of such optimization problems.Article Citation Count: 53Best Proximity Points for Generalized α-ψ-Proximal Contractive Type Mappings(Hindawi Ltd, 2013) Karapınar, Erdal; Karapinar, Erdal; Samet, Bessem; MathematicsWe 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 Count: 73Discussion on Some Coupled Fixed Point Theorems(Springer international Publishing Ag, 2013) Samet, Bessem; Karapınar, Erdal; Karapinar, Erdal; Aydi, Hassen; Rajic, Vesna Cojbasic; MathematicsIn 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 Count: 9Fixed Point Results for Almost Generalized Cyclic (ψ, Φ)-Weak Contractive Type Mappings With Applications(Hindawi Publishing Corporation, 2012) Jleli, Mohamed; Karapınar, Erdal; Karapinar, Erdal; Samet, Bessem; MathematicsWe define a class of almost generalized cyclic (psi,phi)-weak contractive mappings and discuss the existence and uniqueness of fixed points for such mappings. We present some examples to illustrate our results. Moreover, we state some applications of our main results in nonlinear integral equations.Article Citation Count: 23Fixed Point Results for Α-ψλ-contractions on Gauge Spaces and Applications(Hindawi Publishing Corporation, 2013) Jleli, Mohamed; Karapınar, Erdal; Karapinar, Erdal; Samet, Bessem; MathematicsWe extend the concept of alpha-psi-contractive mappings introduced recently by Samet et al. (2012) to the setting of gauge spaces. New fixed point results are established on such spaces, and some applications to nonlinear integral equations on the half-line are presented.Article Citation Count: 8Fixed Point Theorems for Various Classes of Cyclic Mappings(Hindawi Ltd, 2012) Karapınar, Erdal; Karapinar, Erdal; Samet, Bessem; MathematicsWe 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 Count: 58Fixed Points for Generalized (α, Ψ)-Contractions on Generalized Metric Spaces(Springeropen, 2014) Aydi, Hassen; Karapınar, Erdal; Karapinar, Erdal; Samet, Bessem; MathematicsIn 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 Count: 78Further Generalizations of the Banach Contraction Principle(Springeropen, 2014) Jleli, Mohamed; Karapınar, Erdal; Karapinar, Erdal; Samet, Bessem; MathematicsWe 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 Count: 16Further Remarks on Fixed-Point Theorems in the Context of Partial Metric Spaces(Hindawi Ltd, 2013) Karapınar, Erdal; Karapinar, Erdal; Samet, Bessem; MathematicsNew fixed-point theorems on metric spaces are established, and analogous results on partial metric spaces are deduced. This work can be considered as a continuation of the paper Samet et al. (2013).Article Citation Count: 36Generalized α-ψ contractive mappings in quasi-metric spaces and related fixed-point theorems(Springeropen, 2014) Karapınar, Erdal; Karapinar, Erdal; Samet, Bessem; MathematicsIn this paper, we characterize alpha-psi contractive mappings in the setting of quasi-metric spaces and investigate the existence and uniqueness of a fixed point of such mappings. We notice that by using our result some fixed-point theorems in the context of G-metric space can be deduced.Article Citation Count: 105Generalized Α-Ψ Contractive Type Mappings and Related Fixed Point Theorems With Applications(Hindawi Publishing Corporation, 2012) Karapinar, Erdal; Karapınar, Erdal; Samet, Bessem; MathematicsWe establish fixed point theorems for a new class of contractive mappings. As consequences of our main results, we obtain fixed point theorems on metric spaces endowed with a partial order and fixed point theorems for cyclic contractive mappings. Various examples are presented to illustrate our obtained results.Article Citation Count: 13Matkowski Theorems in the Context of Quasi-Metric Spaces and Consequences on g-metric Spaces(Sciendo, 2016) Karapinar, Erdal; Karapınar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Samet, Bessem; MathematicsIn this paper, we prove the characterization of a Matkowski's theorem in the setting of quasi-metric spaces. As a result, we observe that some recent fixed point results in the context of G-metric spaces are consequences of our main result.Article Citation Count: 14Meir-Keeler Type Contractions on Js-Metric Spaces and Related Fixed Point Theorems(Springer Basel Ag, 2018) Karapinar, Erdal; Karapınar, Erdal; Samet, Bessem; Zhang, Dong; MathematicsWe introduce two classes of Meir-Keeler type contractions in the framework of JS-metric spaces introduced by Jleli and Samet (2015). For each class, a fixed point result is derived. Some interesting consequences which follow from our obtained results are discussed.Article Citation Count: 15A Note on 'ψ-geraghty Type Contractions'(Springer international Publishing Ag, 2014) Karapinar, Erdal; Karapınar, Erdal; Samet, Bessem; MathematicsVery 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 Count: 1A Note on Recent Fixed Point Results Involving g-quasicontractive Type Mappings in Partially Ordered Metric Spaces(Springer international Publishing Ag, 2014) Karapinar, Erdal; Karapınar, Erdal; Samet, Bessem; MathematicsIn 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 Count: 10On Best Proximity Points Under the p-property on Partially Ordered Metric Spaces(Hindawi Publishing Corp, 2013) Jleli, Mohamed; Karapınar, Erdal; Karapinar, Erdal; Samet, Bessem; MathematicsVery recently, Abkar and Gabeleh (2013) observed that some best proximity point results under the P-property can be obtained from the same results in fixed-point theory. In this paper, motivated by this mentioned work, we show that the most best proximity point results on a metric space endowed with a partial order (under the P-property) can be deduced from existing fixed-point theorems in the literature. We present various model examples to illustrate this point of view.Article Citation Count: 3On common fixed points that belong to the zero set of a certain function(int Scientific Research Publications, 2017) Karapınar, Erdal; Samet, Bessem; Shahi, Priya; MathematicsWe provide sufficient conditions under which the set of common fixed points of two self-mappings f, g : X -> X is nonempty, and every common fixed point of f and g is the zero of a given function phi : X -> [0, infinity). Next, we show the usefulness of our obtained result in partial metric fixed point theory. (C) 2017 All rights reserved.Article Citation Count: 14On Cyclic (ψ, Φ)-Contractions in Kaleva-seikkala's Type Fuzzy Metric Spaces(Ios Press, 2014) Jleli, Mohamed; Karapınar, Erdal; Karapinar, Erdal; Samet, Bessem; MathematicsIn this paper we introduce the notion of cyclic (psi, phi)-contractions on fuzzy metric spaces in the sense of Kaleva and Seikkala, and we discuss the existence and uniqueness of fixed points for mappings satisfying such type of contractions.Article Citation Count: 11On the existence of fixed points that belong to the zero set of a certain function(Springer international Publishing Ag, 2015) Karapınar, Erdal; O'Regan, Donal; Samet, Bessem; MathematicsLet 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.
