Calogero Vetro

Common fixed points of generalized contractions on partial metric spaces and an application

Abstract In this paper, common fixed point theorems for four mappings satisfying a generalized nonlinear contraction type condition on partial metric spaces are proved. Presented theorems extend the very recent results of I. Altun, F. Sola and H. Simsek [Generalized contractions on partial metric spaces, Topology and its applications 157 (18) (2010) 2778–2785]. As application, some homotopy results for operators on a set endowed with a partial metric are given.

Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces

We prove some coincidence and common fixed point results for three mappings satisfying a generalized weak contractive condition in ordered partial metric spaces. As application of the presented results, we give a unique fixed point result for a mapping satisfying a weak cyclical contractive condition. We also provide some illustrative examples.MSC:47H10, 54H25.

On generalized weakly G-contraction mapping in G-metric spaces

In this paper, we establish some common fixed point results for two self-mappings f and g on a generalized metric space X. To prove our results we assume that f is a generalized weakly G-contraction mapping of types A and B with respect to g.

Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces

The purpose of this paper is to present some fixed point theorems for T-weakly isotone increasing mappings which satisfy a generalized nonlinear contractive condition in complete ordered metric spaces. As application, we establish an existence theorem for a solution of some integral equations.

Coupled fixed point results in cone metric spaces for -compatible mappings

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 Classifications: 54H25; 47H10.

Best proximity point theorems for rational proximal contractions

We provide sufficient conditions which warrant the existence and uniqueness of the best proximity point for two new types of contractions in the setting of metric spaces. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory. We also give some examples to illustrate and validate our definitions and results.MSC:41A65, 46B20, 47H10.

Fixed points in weak non-Archimedean fuzzy metric spaces

Mihet [Fuzzy @j-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems, 159 (2008) 739-744] proved a theorem which assures the existence of a fixed point for fuzzy @j-contractive mappings in the framework of complete non-Archimedean fuzzy metric spaces. Motivated by this, we introduce a notion of weak non-Archimedean fuzzy metric space and prove that the weak non-Archimedean fuzzy metric induces a Hausdorff topology. We utilize this new notion to obtain some common fixed point results for a pair of generalized contractive type mappings.

From metric spaces to partial metric spaces

Motivated by experience from computer science, Matthews (1994) introduced a nonzero self-distance called a partial metric. He also extended the Banach contraction principle to the setting of partial metric spaces. In this paper, we show that fixed point theorems on partial metric spaces (including the Matthews fixed point theorem) can be deduced from fixed point theorems on metric spaces. New fixed point theorems on metric spaces are established and analogous results on partial metric spaces are deduced.MSC:47H10, 54H25.

Common fixed point theorems for families of occasionally weakly compatible mappings

We prove some common fixed point theorems in probabilistic semi-metric spaces for families of occasionally weakly compatible mappings. We also give a common fixed point theorem for mappings satisfying an integral-type implicit relation.

A fixed point theorem for a family of mappings in a fuzzy metric space

In this paper we give a common fixed point theorem for a family of mappings of a G-complete fuzzy metric space (X, M, *) into itself. From this result we deduce a common fixed point theorem for a family of mappings of a complete metric space (X, d) into itself.