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Article Citation - WoS: 20Citation - Scopus: 49Coupled Coincidence Points in Partially Ordered Cone Metric Spaces With a c-distance(Hindawi Ltd, 2012) Shatanawi, Wasfi; Karapinar, Erdal; Aydi, HassenCho et al. (2012) proved some coupled fixed point theorems in partially ordered cone metric spaces by using the concept of a c-distance in cone metric spaces. In this paper, we prove some coincidence point theorems in partially ordered cone metric spaces by using the notion of a c-distance. Our results generalize several well-known comparable results in the literature. Also, we introduce an example to support the usability of our results.Article Citation - WoS: 3Citation - Scopus: 7Some Almost Generalized (ψ, Φ)-Contractions in g-metric Spaces(Hindawi Ltd, 2013) Aydi, Hassen; Amor, Sana Hadj; Karapinar, ErdalIn this paper, we introduce some almost generalized (psi, phi)-contractions in the setting of G-metric spaces. We prove some fixed points results for such contractions. The presented theorems improve and extend some known results in the literature. An example is also presented.Article Citation - WoS: 11Citation - Scopus: 8Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized Meir-Keeler Type Contractions(Hindawi Ltd, 2012) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.We prove coupled coincidence point and coupled fixed point results of F : X x X -> X and g : X -> X involving Meir-Keeler type contractions on the class of partially ordered metric spaces. Our results generalize some recent results in the literature. Also, we give some illustrative examples and application.Article Citation - WoS: 9Citation - Scopus: 13Best Proximity Point Results for Mk-Proximal Contractions(Hindawi Publishing Corporation, 2012) Jleli, Mohamed; Karapinar, Erdal; Samet, BessemLet 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 - WoS: 10Citation - Scopus: 11Fixed Point Theorems Via Auxiliary Functions(Hindawi Publishing Corporation, 2012) Karapinar, Erdal; Salimi, PeymanWe prove new fixed point theorems in the framework of partially ordered metric spaces. The main result is an extension and a generalization of many existing results in the literature. An example is also considered to illustrate the main result.Article Citation - WoS: 40Citation - Scopus: 52Discussion on Generalized-(αψ, Βφ)-Contractive Mappings Via Generalized Altering Distance Function and Related Fixed Point Theorems(Hindawi Ltd, 2014) Berzig, Maher; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-FranciscoWe extend the notion of (alpha psi, beta phi)-contractive mapping, a very recent concept by Berzig and Karapinar. This allows us to consider contractive conditions that generalize a wide range of nonexpansive mappings in the setting of metric spaces provided with binary relations that are not necessarily neither partial orders nor preorders. Thus, using this kind of contractive mappings, we show some related fixed point theorems that improve some well known recent results and can be applied in a variety of contexts.Article Citation - WoS: 1Citation - Scopus: 18Periodic Points of Weaker Meir-Keeler Contractive Mappings on Generalized Quasimetric Spaces(Hindawi Publishing Corporation, 2014) Lin, Ing-Jer; Chen, Chi-Ming; Karapinar, ErdalBy using the weaker Meir-Keeler function phi and the triangular alpha-admissible mapping alpha, we introduce the notion of (alpha - phi)-weaker Meir-Keeler contractive mappings and prove a theorem which assures the existence of a periodic point for these mappings on generalized quasimetric spaces.Article Citation - WoS: 43Coupled Fixed Points for Meir-Keeler Contractions in Ordered Partial Metric Spaces(Hindawi Ltd, 2012) Abdeljawad, Thabet; Aydi, Hassen; Karapinar, ErdalIn this paper, we prove the existence and uniqueness of a new Meir-Keeler type coupled fixed point theorem for two mappings F : X x X -> X and g : X -> X on a partially ordered partial metric space. We present an application to illustrate our obtained results. Further, we remark that the metric case of our results proved recently in Gordji et al. (2012) have gaps. Therefore, our results revise and generalize some of those presented in Gordji et al. (2012)Article Citation - WoS: 16Citation - Scopus: 16A Generalized Meir-Keeler Contraction on Partial Metric Spaces(Hindawi Ltd, 2012) Aydi, Hassen; Karapinar, Erdal; Rezapour, ShahramWe introduce a generalization of the Meir-Keeler-type contractions, referred to as generalized Meir-Keeler-type contractions, over partial metric spaces. Moreover, we show that every orbitally continuous generalized Meir-Keeler-type contraction has a fixed point on a 0-complete partial metric space.Article Citation - WoS: 25Citation - Scopus: 22Tripled Fixed Points of Multivalued Nonlinear Contraction Mappings in Partially Ordered Metric Spaces(Hindawi Publishing Corporation, 2011) Abbas, Mujahid; Aydi, Hassen; Karapinar, ErdalBerinde and Borcut (2011), introduced the concept of tripled fixed point for single mappings in partially ordered metric spaces. Samet and Vetro (2011) established some coupled fixed point theorems for multivalued nonlinear contraction mappings in partially ordered metric spaces. In this paper, we obtain existence of tripled fixed point of multivalued nonlinear contraction mappings in the framework of partially ordered metric spaces. Also, we give an example.
