  This paper studies the properties of convergence of distances between points
and the existence and uniqueness of best proximity and fixed points of the
so-called semi-cyclic impulsive self-mappings on the union of a number of
nonempty subsets in metric spaces. The concept of semi-cyclic self- mappings
generalizes the well-known of cyclic ones in the sense that the iterated
sequences built through such mappings are allowed to have images located in the
same subset as its pre-image. The self-mappings under study may be impulsive
since eventually being composite mappings involving two self-mappings, one of
them being eventually discontinuous so that the formalism can potentially be
applied to the study of stability of a class of impulsive differential
equations and their discrete counterparts
