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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: 59Citation - Scopus: 68Generalized (c)-conditions and Related Fixed Point Theorems(Pergamon-elsevier Science Ltd, 2011) Karapinar, Erdal; Tas, Kenan; Karapnar, ErdalIn this manuscript, the notion of C-condition [K. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095] is generalized. Some new fixed point theorems are obtained. (C) 2011 Elsevier Ltd. All rights reserved.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: 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: 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: 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: 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.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.Article Citation - WoS: 167Citation - Scopus: 168Fixed Point Theorems for Operators on Partial Metric Spaces(Pergamon-elsevier Science Ltd, 2011) Karapinar, Erdal; Erhan, Inci M.; Karapnar, ErdalFixed point theorems for operators of a certain type on partial metric spaces are given. Orbitally continuous operators on partial metric spaces and orbitally complete partial metric spaces are defined, and fixed point theorems for these operators are given. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 82Citation - Scopus: 87On Common Fixed Points in g-metric Spaces Using (e.a) Property(Pergamon-elsevier Science Ltd, 2012) Mustafa, Zead; Aydi, Hassen; Karapinar, Erdal; Karapnar, ErdalIn this paper, we introduce some new types of pairs of mappings (f, g) on G-metric spaces called G-weakly commuting of type G(f) and G-R-weakly commuting of type G(f). We obtain also several common fixed point results by using the (E.A) property. (c) 2012 Elsevier Ltd. All rights reserved.
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