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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: 6Citation - Scopus: 5α-(ψ, φ) Contractive mappings on quasi-partial metric spaces(Springer international Publishing Ag, 2015) Karapinar, Erdal; Gholizadeh, Leila; Alsulami, Hamed H.; Noorwali, MahaIn this paper, we consider alpha- contractive mappings in the setting of quasi-partial metric spaces and verify the existence of a fixed point on such spaces. Moreover, we present some examples and applications in integral equations of our obtained results.Article Citation - WoS: 13Citation - Scopus: 11Some Fixed Point Results on Quasi-b-metric-like Spaces(Springer international Publishing Ag, 2015) Cvetkovic, Marija; Karapinar, Erdal; Rakocevic, VladimirIn this paper, we investigate the existence and uniqueness of a fixed point of certain operators in the setting of complete quasi-b-metric-like spaces via admissible mappings. Our results improve, extend, and unify several well-known existence results.Article Citation - WoS: 14Citation - Scopus: 24Generalized Alpha-Psi Type Mappings of Integral Type and Related Fixed Point Theorems(Springer, 2014) Karapinar, Erdal; Shahi, Priya; Tas, KenanThe aim of this paper is to introduce two classes of generalized alpha-psi-contractive type mappings of integral type and to analyze the existence of fixed points for these mappings in complete metric spaces. Our results are improved versions of a multitude of relevant fixed point theorems of the existing 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: 10Citation - Scopus: 15Fixed Points of Generalized Contractive Mappings of Integral Type(Springer international Publishing Ag, 2014) Alsulami, Hamed H.; Karapinar, Erdal; O'Regan, Donal; Shahi, PriyaThe aim of this paper is to introduce classes of alpha-admissible generalized contractive type mappings of integral type and to discuss the existence of fixed points for these mappings in complete metric spaces. Our results improve and generalize fixed point results in the literature.Article Citation - WoS: 20Citation - Scopus: 28Some Extensions for Geragthy Type Contractive Mappings(Springer international Publishing Ag, 2015) Karapinar, Erdal; Alsulami, Hamed H.; Noorwali, MahaIn this paper, we establish some fixed point theorems on some extensions of Geragthy contractive type mappings in the context of b-metric-like spaces.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.
