Browsing by Author "Aydi, Hassen"
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Editorial Citation Count: 0Advances on Multivalued Operators and Related Fixed Point Problems(Hindawi Publishing Corporation, 2014) Karapınar, Erdal; Karapinar, Erdal; Du, Wei-Shih; Aydi, Hassen; Romaguera, Salvador; Mathematics[No Abstract Available]Article Citation Count: 22Berinde-Type Generalized Contractions on Partial Metric Spaces(Hindawi Ltd, 2013) Karapınar, Erdal; Amor, Sana Hadj; Karapinar, Erdal; MathematicsWe consider generalized Berinde-type contractions in the context of partial metric spaces. Such contractions are also known as generalized almost contractions in the literature. In this paper, we extend, generalize, and enrich the results in this direction. Some examples are presented to illustrate our results.Article Citation Count: 23Best proximity points and extension of Mizoguchi-Takahashi's fixed point theorems(Springer int Publ Ag, 2013) Karapınar, Erdal; Aydi, Hassen; Karapinar, Erdal; Sintunavarat, Wutiphol; MathematicsIn this paper, we introduce a multi-valued cyclic generalized contraction by extending the Mizoguchi and Takahashi's contraction for non-self mappings. We also establish a best proximity point for such type contraction mappings in the context of metric spaces. Later, we characterize this result to investigate the existence of best proximity point theorems in uniformly convex Banach spaces. We state some illustrative examples to support our main theorems. Our results extend, improve and enrich some celebrated results in the literature, such as Nadler's fixed point theorem, Mizoguchi and Takahashi's fixed point theorem.Article Citation Count: 19Best proximity points of generalized almost ψ-Geraghty contractive non-self-mappings(Springer international Publishing Ag, 2014) Erhan, İnci; Karapinar, Erdal; Karapınar, Erdal; Salimi, Peyman; MathematicsIn 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 Count: 37Common fixed points for generalized -implicit contractions in partial metric spaces: consequences and application(Springer-verlag Italia Srl, 2015) Karapınar, Erdal; Jellali, Manel; Karapinar, Erdal; MathematicsIn this paper, we introduce the concept of generalized -admissible pair of mappings generalizing the definition of -admissible mappings presented by Samet et al. (Nonlinear Anal 75:2154-2165, 2012). Based on above, we define generalized -implicit contractions in the setting of partial metric spaces and we provide some common fixed point results for such contractions. We also derive some consequences and corollaries from our obtained results. An application and some examples are presented making effective the new concepts and results.Article Citation Count: 89Common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in -metric spaces(Springer int Publ Ag, 2012) Karapınar, Erdal; Aydi, Hassen; Karapinar, Erdal; Shatanawi, Wasfi; MathematicsIn this article, we establish some common fixed point theorems for a hybrid pair {} of single valued and multi-valued maps satisfying a generalized contractive condition defined on -metric spaces. Our results unify, generalize and complement various known comparable results from the current literature. 54H25; 47H10; 54E50.Article Citation Count: 11Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized Meir-Keeler Type Contractions(Hindawi Ltd, 2012) Erhan, İnci; Karapinar, Erdal; Karapınar, Erdal; MathematicsWe 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 Count: 19Coupled coincidence point results on generalized distance in ordered cone metric spaces(Springer, 2013) Karapınar, Erdal; Karapinar, Erdal; Mustafa, Zead; MathematicsIn this paper, we establish some coupled coincidence point results in the setting of partially ordered cone metric spaces via -distance. We also proved some related coupled common fixed point theorems for such mappings. Our results generalize, extend, and unify several well-known comparable results in the literature regarding this topic. We present some examples to illustrate the concepts and results.Article Citation Count: 19Coupled Coincidence Points in Partially Ordered Cone Metric Spaces with a c-Distance(Hindawi Ltd, 2012) Karapınar, Erdal; Karapinar, Erdal; Aydi, Hassen; MathematicsCho 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 Count: 143Coupled fixed point results for (ψ, φ)-weakly contractive condition in ordered partial metric spaces(Pergamon-elsevier Science Ltd, 2011) Karapınar, Erdal; Karapinar, Erdal; Shatanawi, Wasfi; MathematicsIn this paper, we prove some coupled fixed point theorems involving a (psi, phi)-weakly contractive condition for mapping having the mixed monotone property in ordered partial metric spaces. These results are analogous to theorems of Van Luong and Xuan Thuan (2011) [10] on the class of ordered partial metric spaces. Also, an application is given to support our results. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation Count: 42Coupled Fixed Points for Meir-Keeler Contractions in Ordered Partial Metric Spaces(Hindawi Ltd, 2012) Karapınar, Erdal; Aydi, Hassen; Karapinar, Erdal; MathematicsIn 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 Count: 26A discussion on generalized almost contractions via rational expressions in partially ordered metric spaces(Springeropen, 2014) Karapınar, Erdal; Karapinar, Erdal; Aydi, Hassen; MathematicsThe 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 Count: 73Discussion on some coupled fixed point theorems(Springer international Publishing Ag, 2013) 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: 6Existence of Solutions for a Periodic Boundary Value Problem via Generalized Weakly Contractions(Hindawi Ltd, 2013) Karapınar, Erdal; Karapinar, Erdal; Aydi, Hassen; MathematicsWe discuss the existence of solutions for a periodic boundary value problem and for some polynomials. For this purpose, we present some fixed point theorems for weakly and generalized weakly contractive mappings in the setting of partially ordered complete metric spaces.Article Citation Count: 23Fixed point results on a class of generalized metric spaces(Springer Heidelberg, 2012) Karapınar, Erdal; Karapinar, Erdal; Lakzian, Hossein; MathematicsBrianciari ('A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces,' Publ. Math. Debrecen 57 (2000) 31-37) initiated the notion of the generalized metric space as a generalization of a metric space in such a way that the triangle inequality is replaced by the 'quadrilateral inequality,' d(x, y) <= d(x, a) + d(a, b) + d(b, y) for all pairwise distinct points x, y, a, and b of X. In this paper, we establish a fixed point result for weak contractive mappings T : X -> X in complete Hausdorff generalized metric spaces. The obtained result is an extension and a generalization of many existing results in the literature.Article Citation Count: 218A fixed point theorem for set-valued quasi-contractions in b-metric spaces(Springer international Publishing Ag, 2012) Karapınar, Erdal; Bota, Monica-Felicia; Karapinar, Erdal; Mitrovic, Slobodanka; MathematicsIn this article, we give a fixed point theorem for set-valued quasi-contraction maps in b-metric spaces. This theorem extends, unifies and generalizes several well known comparable results in the existing literature.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) 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: 27Generalized Meir-Keeler type contractions on G-metric spaces(Elsevier Science inc, 2013) Karapınar, Erdal; Aydi, Hassen; Karapinar, Erdal; MathematicsIn this manuscript, we introduce generalized Meir-Keeler type contractions over G-metric spaces. Moreover, we show that every orbitally continuous generalized Meir-Keeler type contraction has a unique fixed point on complete G-metric spaces. We illustrate our results by some given examples. (C) 2013 Elsevier Inc. All rights reserved.Article Citation Count: 16A Generalized Meir-Keeler-Type Contraction on Partial Metric Spaces(Hindawi Ltd, 2012) Karapınar, Erdal; Karapinar, Erdal; Rezapour, Shahram; MathematicsWe 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.
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