Browsing by Author "Roldan, Antonio"

Now showing 1 - 4 of 4

Citation - WoS: 30
Citation - Scopus: 35
Discussion 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, Wutiphol
After 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.
Citation - WoS: 8
Citation - Scopus: 11
g-metric Spaces in Any Number of Arguments and Related Fixed-Point Theorems
(Springer international Publishing Ag, 2014) Roldan, Antonio; Karapinar, Erdal; Kumam, Poom
Inspired 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.
Citation - WoS: 34
Citation - Scopus: 43
Meir-Keeler Type Multidimensional Fixed Point Theorems in Partially Ordered Metric Spaces
(Hindawi Ltd, 2013) Karapinar, Erdal; Roldan, Antonio; Martinez-Moreno, Juan; Roldan, Concepcion
We study the existence and uniqueness of a fixed point of the multidimensional operators which satisfy Meir-Keeler type contraction condition. Our results extend, improve, and generalize the results mentioned above and the recent results on these topics in the literature.
Citation - WoS: 11
Citation - Scopus: 5
A 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, Juan
In 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.