Fixed Point Theorems for Various Classes of Cyclic Mappings

We introduce new classes of cyclic mappings and we study the existence and uniqueness of fixed points for such mappings. The presented theorems generalize and improve several existing results in the literature

On Weak Contractive Cyclic Maps in Generalized Metric Spaces and Some Related Results on Best Proximity Points and Fixed Points

This paper discusses the properties of convergence of sequences to limit cycles defined by best proximity points of adjacent subsets for two kinds of weak contractive cyclic maps defined by composite maps built with decreasing functions with either the so-called r-weaker Meir-Keeler or r,r0-stronger Meir-Keeler functions in generalized metric spaces. Particular results about existence and uniqueness of fixed points are obtained for the case when the sets of the cyclic disposal have a nonempty intersection. Illustrative examples are discussed

Periodic Points and Fixed Points for the Weaker (

We introduce the notion of weaker (ϕ,φ)-contractive mapping in complete metric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature

Fixed Point and Best Proximity Theorems under Two Classes of Integral-Type Contractive Conditions in Uniform Metric Spaces

This paper investigates the existence of fixed points and best proximity points of p-cyclic self-maps on a set of subsets of a certain uniform space under integral-type contractive conditions. The parallel properties of the associated restricted composed maps from any of the subsets to itself are also investigated. The subsets of the uniform space are not assumed to intersect.Ministerio de Educación (DPI2009-07197) y Gobierno Vasco (IT378-10

On fixed points and convergence results of sequences generated by uniformly convergent and point-wisely convergent sequences of operators in Menger probabilistic metric spaces

Altres ajuts: The authors thank the reviewers for their useful comments and to University Jorge Tadeo Lozano by its support through Grant 644-11-14.In the framework of complete probabilistic Menger metric spaces, this paper investigates some relevant properties of convergence of sequences built through sequences of operators which are either uniformly convergent to a strict k -contractive operator, for some real constant k ∈ (0, 1), or which are strictly k -contractive and point-wisely convergent to a limit operator. Those properties are also reformulated for the case when either the sequence of operators or its limit are strict -contractions. The definitions of strict (k and ) contractions are given in the context of probabilistic metric spaces, namely in particular, for the considered probability density function. A numerical illustrative example is discussed

Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces

This paper presents some results concerning the properties of distances and existence and uniqueness of best proximity points of p-cyclic proximal, weak proximal contractions, and some of their generalizations for the non-self-mapping T:⋃i∈p-Ai→⋃i∈p-Bi  (p≥2), where Ai and Bi, ∀i∈p-={1,2,…,p}, are nonempty subsets of X which satisfy TAi⊆Bi,∀i∈p-, such that (X,d) is a metric space. The boundedness and the convergence of the sequences of distances in the domains and in their respective image sets of the cyclic proximal and weak cyclic proximal non-self-mapping, and of some of their generalizations are investigated. The existence and uniqueness of the best proximity points and the properties of convergence of the iterates to such points are also addressed