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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: 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: 33Citation - Scopus: 31Discussion on "multidimensional Coincidence Points" Via Recent Publications(Hindawi Ltd, 2014) Al-Mezel, Saleh A.; Alsulami, Hamed H.; Karapinar, Erdal; Lopez-de-Hierro, Antonio-Francisco Roldan; Karapnar, ErdalWe show that some definitions of multidimensional coincidence points are not compatible with the mixed monotone property. Thus, some theorems reported in the recent publications (Dalal et al., 2014 and Imdad et al., 2013) have gaps. We clarify these gaps and we present a new theorem to correct the mentioned results. Furthermore, we show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem.Editorial New Contribution To the Advancement of Fixed Point Theory, Equilibrium Problems, and Optimization Problems(Hindawi Publishing Corporation, 2013) Du, Wei-Shih; Karapinar, Erdal; Lin, Lai-Jiu; Lee, Gue Myung; Tanaka, Tamaki; Karapnar, Erdal[No Abstract Available]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: 9Citation - Scopus: 13Best Proximity Point Results for Mk-Proximal Contractions(Hindawi Publishing Corporation, 2012) Jleli, Mohamed; Karapinar, Erdal; Samet, Bessem; Karapnar, ErdalLet 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: 20Citation - Scopus: 49Coupled Coincidence Points in Partially Ordered Cone Metric Spaces With a c-distance(Hindawi Ltd, 2012) Shatanawi, Wasfi; Karapinar, Erdal; Aydi, Hassen; Karapnar, ErdalCho 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.
