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Article Citation - WoS: 16Citation - Scopus: 17A Generalized Meir-Keeler Contraction on Partial Metric Spaces(Hindawi Ltd, 2012) Aydi, Hassen; Karapinar, Erdal; Rezapour, Shahram; Karapnar, ErdalWe 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: 7Citation - Scopus: 9On Cyclic Generalized Weakly c-contractions on Partial Metric Spaces(Hindawi Ltd, 2013) Karapinar, Erdal; Rakocevic, Vladimir; Karapnar, ErdalWe give new results of a cyclic generalized weakly C-contraction in partial metric space. The results of this paper extend, generalize, and improve some fixed point theorems in the literature.Article Citation - WoS: 143Citation - Scopus: 141Coupled Fixed Point Results for (ψ, Φ)-Weakly Contractive Condition in Ordered Partial Metric Spaces(Pergamon-elsevier Science Ltd, 2011) Aydi, Hassen; Karapinar, Erdal; Shatanawi, Wasfi; Karapnar, ErdalIn 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 - WoS: 52Citation - Scopus: 69Quadruple Fixed Point Theorems for Nonlinear Contractions(Pergamon-elsevier Science Ltd, 2012) Karapinar, Erdal; Nguyen Van Luong; Luong, Nguyen Van; Karapnar, ErdalThe notion of coupled fixed point is introduced by Gnana-Bhaskar and Lakshmikantham. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut. In this manuscript, a quadruple fixed point is considered and some new related fixed point theorems are obtained. We also give some examples to illustrate our results. (c) 2012 Elsevier Ltd. All rights reserved.Article Citation - WoS: 31Citation - Scopus: 36New Meir-Keeler Type Tripled Fixed-Point Theorems on Ordered Partial Metric Spaces(Hindawi Ltd, 2012) Aydi, Hassen; Karapinar, Erdal; Karapnar, ErdalIn this paper, we prove some new Meir-Keeler type tripled fixed-point theorems on a partially ordered complete partial metric space. Also, as application, some results of integral type are given.Article Citation - WoS: 25Citation - Scopus: 36Fixed Point Results for Α-ψλ-contractions on Gauge Spaces and Applications(Hindawi Publishing Corporation, 2013) Jleli, Mohamed; Karapinar, Erdal; Samet, Bessem; Karapnar, ErdalWe 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 - WoS: 30Citation - Scopus: 37Θ-Metric Space: a Generalization(Hindawi Ltd, 2013) Khojasteh, Farshid; Karapınar, Erdal; Karapinar, Erdal; Radenovic, Stojan; Karapınar, Erdal; Karapnar, Erdal; Mathematics; MathematicsWe introduce the notion of theta-metric as a generalization of a metric by replacing the triangle inequality with a more generalized inequality. We investigate the topology of the spaces induced by a theta-metric and present some essential properties of it. Further, we give characterization of well-known fixed point theorems, such as the Banach and Caristi types in the context of such spaces.Article Citation - WoS: 50Citation - Scopus: 48Some Common Fixed Point Theorems in Partial Metric Spaces(Hindawi Ltd, 2011) Karapinar, Erdal; Yuksel, Ugur; Karapnar, ErdalMany problems in pure and applied mathematics reduce to a problem of common fixed point of some self-mapping operators which are defined on metric spaces. One of the generalizations of metric spaces is the partial metric space in which self-distance of points need not to be zero but the property of symmetric and modified version of triangle inequality is satisfied. In this paper, some well-known results on common fixed point are investigated and generalized to the class of partial metric spaces.Editorial Advances on Multivalued Operators and Related Fixed Point Problems(Hindawi Publishing Corporation, 2014) Chen, Chi-Ming; Karapinar, Erdal; Du, Wei-Shih; Aydi, Hassen; Romaguera, Salvador; Karapnar, Erdal[No Abstract Available]Article Citation - WoS: 40Citation - Scopus: 46Some Fixed Point Results for Multi-Valued Mappings in b-metric Spaces(Springeropen, 2014) Kutbi, Marwan Amin; Karapinar, Erdal; Ahmad, Jamshaid; Azam, Akbar; Karapnar, ErdalThe aim of this paper is to establish some fixed point theorems for set-valued mappings in the context of b-metric spaces. The proposed theorems expand and generalize several well-known comparable results in the literature. An example is also given to support our main result.
