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Article Citation - WoS: 3Citation - Scopus: 4A New Class of Generalized Contraction Using p-functions in Ordered Metric Spaces(Sciendo, 2015) Amor, Sana Hadj; Karapinar, Erdal; Kumam, PoomIn this paper, we introduced and studied a new class of mappings in ordered metric spaces that is inspired from the concept of a P-function introduced in Chaipunya et. al. [10]. With our new class, we furnish fixed point theorems for continuous, noncontinuous, monotonic, and nonmonotonic mappings in various kinds of the ordering structures.Article Citation - WoS: 8Citation - Scopus: 11g-metric Spaces in Any Number of Arguments and Related Fixed-Point Theorems(Springer international Publishing Ag, 2014) Roldan, Antonio; Karapinar, Erdal; Kumam, PoomInspired by the notion of Mustafa and Sims' G-metric space and the attention that this kind of metric has received in recent times, we introduce the concept of a G-metric space in any number of variables, and we study some of the basic properties. Then we prove that the family of this kind of metric is closed under finite products. Finally, we show some fixed-point theorems that improve and extend some well-known results in this field.Article Citation - WoS: 16Citation - Scopus: 19Fixed Point Theorems in Quasi-Metric Spaces and Applications To Multidimensional Fixed Point Theorems on g-metric Spaces(Yokohama Publ, 2015) Agarwal, Ravi; Karapinar, Erdal; Roldan-Lopez-De-Hierro, Antonio-Francisco; MathematicsIn this manuscript, we investigate the equivalence of the coupled fixed point theorems in quasi-metric spaces and in G-metric spaces. We also notice that coupled fixed point theorems in the setting of G-metric spaces can be derived from their corresponding versions in quasi-metric spaces. Our results generalize and unify several fixed point theorems in the context of G-metric spaces in the literature.Article Citation - WoS: 30Citation - Scopus: 35Discussion of Coupled and Tripled Coincidence Point Theorems for Φ-Contractive Mappings Without the Mixed g-monotone Property(Springer international Publishing Ag, 2014) Karapinar, Erdal; Roldan, Antonio; Shahzad, Naseer; Sintunavarat, WutipholAfter the appearance of Ran and Reuring's theorem and Nieto and Rodriguez-Lopez's theorem, the field of fixed point theory applied to partially ordered metric spaces has attracted much attention. Coupled, tripled, quadrupled and multidimensional fixed point results has been presented in recent times. One of the most important hypotheses of these theorems was the mixed monotone property. The notion of invariant set was introduced in order to avoid the condition of mixed monotone property, and many statements have been proved using these hypotheses. In this paper we show that the invariant condition, together with transitivity, lets us to prove in many occasions similar theorems to which were introduced using the mixed monotone property.Article Citation - WoS: 11Citation - Scopus: 5A Note on 'n-fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces'(Springer int Publ Ag, 2013) Karapinar, Erdal; Roldan, Antonio; Roldan, Concepcion; Martinez-Moreno, JuanIn this note we prove that a kind of mappings depending on k arguments introduced in (Paknazar et al. in Fixed Point Theory Appl. 2013: 111, 2013) only depend on their first argument. Therefore, results in that paper reduce to the unidimensional case. We also include some commentaries about the different notions of multidimensional fixed point.Article Citation - WoS: 1Tripled Fixed Point Theorems in Partially Ordered Metric Spaces(Univ Babes-bolyai, 2013) Karapinar, ErdalThe notion of tripled fixed point is introduced by Berinde and Borcut [1]. In this manuscript, some new tripled fixed point theorems are obtained by using a generalization of the results of Luong and Thuang [11].
