Search results for "metric space"
showing 10 items of 316 documents
An amalgamation property for metric spaces
2016
In this paper we show that sufficiently similar finite metric spaces can be amalgamated so that the distance between them is sufficiently small.
Coupled fixed point results in cone metric spaces for -compatible mappings
2011
In this paper, we introduce the concepts of -compatible mappings, b-coupled coincidence point and b-common coupled fixed point for mappings F, G : X × X → X, where (X, d) is a cone metric space. We establish b-coupled coincidence and b-common coupled fixed point theorems in such spaces. The presented theorems generalize and extend several well-known comparable results in the literature, in particular the recent results of Abbas et al. [Appl. Math. Comput. 217, 195-202 (2010)]. Some examples are given to illustrate our obtained results. An application to the study of existence of solutions for a system of non-linear integral equations is also considered. 2010 Mathematics Subject Classificati…
Coupled fixed point results in cone metric spaces for -compatible mappings
2011
Abstract In this paper, we introduce the concepts of -compatible mappings, b-coupled coincidence point and b-common coupled fixed point for mappings F, G : X × X → X, where (X, d) is a cone metric space. We establish b-coupled coincidence and b-common coupled fixed point theorems in such spaces. The presented theorems generalize and extend several well-known comparable results in the literature, in particular the recent results of Abbas et al. [Appl. Math. Comput. 217, 195-202 (2010)]. Some examples are given to illustrate our obtained results. An application to the study of existence of solutions for a system of non-linear integral equations is also considered. 2010 Mathematics …
Fixed point theorems for α-set-valued quasi-contractions in b-metric spaces
2015
Recently, Samet et al. [B. Samet, C. Vetro and P. Vetro, Fixed point theorems for alpha-psi-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165] introduced the notion of alpha-psi-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notions of alpha-set-valued contraction and alpha-set-valued quasi-contraction and we give some fixed point theorems for such classes of mappings in the setting of b-metric spaces and ordered b-metric spaces. The presented theorems extend, unify and generalize several well-known comparable results in the existing literature.
Fixed point results in cone metric spaces
2010
We prove a result on points of coincidence and common fixed points for three self mappings satisfying a weak generalized contractive type condition in cone metric spaces. We deduce some results on common fixed points for two self mappings satisfying a weak contractive type condition in cone metric spaces. This results generalize some well-known recent results.
On fixed points of Berinde’s contractive mappings in cone metric spaces
2010
In this paper we establish some common fixed point theorems for two self-mappings satisfying a generalized contractive condition. This result generalizes well known comparable results in the literature. As an application, a necessary and sufficient condition for a fixed point to be a periodic point for the mapping involved therein, without appealing to continuity, in a cone metric space is established.
Fixed point results in cone metric spaces for contractions of Zamfirescu type
2010
We prove a result on points of coincidence and common fixed points in cone metric spaces for two self mappings satisfying a weak generalized contractive condition of Zamfirescu type. We deduce some results on common fixed points for two self mappings satisfying a weak contractive type condition. These results generalize some well-known recent results.
Baum-Katz’s Type Theorems for Pairwise Independent Random Elements in Certain Metric Spaces
2020
In this study, some Baum-Katz’s type theorems for pairwise independent random elements are extended to a metric space endowed with a convex combination operation. Our results are considered in the cases of identically distributed and non-identically distributed random elements. Some illustrative examples are provided to sharpen the results. peerReviewed
Coupled coincidence point results for (φ,ψ)-contractive mappings in partially ordered metric spaces
2014
Abstract. In this paper, we extend the coupled coincidence point theorems for a mixed g-monotone operator F : X × X → X $F:X\times X\rightarrow X$ obtained by Alotaibi and Alsulami [Fixed Point Theory Appl. (2011), article ID 44], by weakening the involved contractive condition. Two examples are given to illustrate the effectiveness of our generalizations. Our result also generalizes some recent results announced in the literature. Moreover, some applications to integral equations are presented.
Coupled fixed-point results for T-contractions on cone metric spaces with applications
2015
The notion of coupled fixed point was introduced in 2006 by Bhaskar and Lakshmikantham. On the other hand, Filipovićet al. [M. Filipovićet al., “Remarks on “Cone metric spaces and fixed-point theorems of T-Kannan and T-Chatterjea contractive mappings”,” Math. Comput. Modelling 54, 1467–1472 (2011)] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper we prove some coupled fixed-point theorems for certain T-contractions and study the existence of solutions of a system of nonlinear integral equations using the results of our work. The results of this paper extend and generalize well-known comparable results in the literature.