Fixed points and best proximity points in contractive cyclic self-maps satisfying constraints in closed integral form with some applications

This paper investigates the existence of best proximity points and the potential fixed points of p-cyclic self-maps which are defined on the union of a finite set of subsets of a certain uniform metric space under several integral-type contractive conditions. The corresponding properties of the associated restricted composed maps from any of the subsets to itself are also dealt with in a formal context. The above subsets of the uniform metric space are not assumed to necessarily intersect but the case when they intersect leads to particular results of the general case in the sense that best proximity points become fixed points. Common fixed points and best proximity points of pairs of self-maps on the above subsets of the uniform metric space are also investigated. © 2012 Elsevier Ltd All rights reserved.