Common fixed points in cone metric spaces

In this paper we consider a notion of g-weak contractive mappings in the setting of cone metric spaces and we give results of common fixed points. This results generalize some common fixed points results in metric spaces and some of the results of Huang and Zhang in cone metric spaces. Supported by Universitá degli Studi di Palermo, R. S. ex 60%.     

Coupled fixed points in partially ordered metric spaces and application

In this paper, we prove some coupled fixed point theorems for mappings having a mixed monotone property in partially ordered metric spaces. The main results of this paper are generalizations of the main results of Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379-1393]. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.     

Group actions on metric spaces: fixed points and free subgroups

We look at group actions on graphs and other metric spaces, e. g., at group actions on geodesic hyperbolic spaces. We classify the types of automorphisms on these spaces and prove several results about the density of the hyperbolic limit set of the group in the whole limit set of the group.     

Common fixed points for R-weakly commuting in fuzzy metric spaces

In this paper, we study the concept of R-weakly commuting of type (A _g ) of Pathak et?al. (Bull Korean Math Soc 34:247?C257, 1997) in fuzzy metric spaces. We also establish the existence of common fixed point theorems by using the common limit in the range property and give an example to validate our the main results.     

Common fixed points for discontinuous mappings in fuzzy metric spaces

In this paper we prove some common fixed point theorems for fuzzy contraction respect to a mapping, which satisfies a condition of weak compatibility. We deduce also fixed point results for fuzzy contractive mappings in the sense of Gregori and Sapena. The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.     

Common fixed points for four maps in cone metric spaces

The existence of coincidence points and common fixed points for four mappings satisfying generalized contractive conditions without exploiting the notion of continuity of any map involved therein, in a cone metric space is proved. These results extend, unify and generalize several well known comparable results in the existing literature.     

Common fixed points of two maps in cone metric spaces

We prove the existence of points of coincidence and common fixed points of a pair of self-mappings satisfying a generalized contractive condition in cone metric spaces. Our results generalize several well-known recent and classical results.      

Banach operator pairs and common fixed points in hyperconvex metric spaces

The purpose of this paper is to establish DeMarr’s well-known theorem for an arbitrary family of symmetric Banach operator pairs in hyperconvex metric spaces without the compactness assumption. We also give necessary and sufficient criteria for the existence of a common fixed point of a semigroup of isometric mappings. As an application, several results on the invariant best approximation are proved.     

Common fixed points of four maps in partially ordered metric spaces

In this paper, common fixed points of four mappings satisfying a generalized weak contractive condition in the framework of partially ordered metric space are obtained. We also provide examples of new concepts introduced herein.     

Hybrid fixed points of multivalued operators in metric spaces with applications

This paper deals with the existence of hybrid fixed points involving two multivalued operators in a complete metric space. Our claim is also illustrated with applications to a class of integral inclusions for proving the existence results.     

Connected extensions of metric spaces and fixed points of Banach contractions

Two theorems announced by the author are proved. The first theorem concerns the existence of connected metrizable extensions of metric spaces. The second theorem is a slightly paradoxical assertion about the validity of the fixed-point principle. Bibliography: 4 titles. Translated fromProblemy Matematicheskogo Analiza, No. 17, 1997, pp. 227–237.     

Haarlet analysis of Lipschitz regularity in metric measure spaces

In this note we shall give a characterization of Lipschitz spaces on spaces of homogeneous type via Haar coefficients.     

Common fixed points for generalized contractive multivalued operators in complete metric spaces

In this paper,we discuss some new fixed point theorems for a pair of multivalued operators which satisfy generalized contractive condition. Our results are the extension and improvement of corresponding results of single-valued operators. Finally, some examples are given to illustrate the usability of our results.     

Common fixed points of almost generalized contractive mappings in ordered metric spaces

The existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved. Some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature.     

Cut points in metric spaces

In this note, we will define topological and virtual cut points of finite metric spaces and show that, though their definitions seem to look rather distinct, they actually coincide. More specifically, let X denote a finite set, and let denote a metric defined on X. The tight span T(D) of D consists of all maps for which f(x)=sup_yX(xy−f(x)) holds for all xX. Define a map fT(D) to be a topological cut point of D if T(D)−{f} is disconnected, and define it to be a virtual cut point of D if there exists a bipartition (or split) of the support of f into two non-empty sets A and B such that ab=f(a)+f(b) holds for all points aA and bB. It will be shown that, for any given metric D, topological and virtual cut points actually coincide, i.e., a map fT(D) is a topological cut point of D if and only if it is a virtual cut point of D.     

Dynamic processes and fixed points of set-valued nonlinear contractions in cone metric spaces

Investigations concerning the existence of dynamic processes convergent to fixed points of set-valued nonlinear contractions in cone metric spaces are initiated. The conditions guaranteeing the existence and uniqueness of fixed points of such contractions are established. Our theorems generalize recent results obtained by Huang and Zhang [L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive maps, J. Math. Anal. Appl. 332 (2007) 1467–1475] for cone metric spaces and by Klim and Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334 (1) (2007) 132–139] for metric spaces. The examples and remarks provided show an essential difference between our results and those mentioned above.