On Some Boundedness and Convergence Properties of a Class of Switching Maps in Probabilistic Metric Spaces with Applications to Switched Dynamic Systems

Altres ajuts: Gobierno Vasco (IT378-10) i Universidad del País Vasco (UFI 2011/07)This paper investigates some boundedness and convergence properties of sequences which are generated iteratively through switched mappings defined on probabilistic metric spaces as well as conditions of existence and uniqueness of fixed points. Such switching mappings are built from a set of primary self-mappings selected through switching laws. The switching laws govern the switching process in between primary self-mappings when constructing the switching map. The primary self-mappings are not necessarily contractive but if at least one of them is contractive then there always exist switching maps which exhibit convergence properties and have a unique fixed point. If at least one of the self-mappings is nonexpansive or an appropriate combination given by the switching law is nonexpansive, then sequences are bounded although not convergent, in general. Some illustrative examples are also given

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