A development of contraction mapping principles on Hausdorff uniform spaces

Abstract

Certain generalized Banach’s contraction mapping principles on metric spaces are unified and/or extended to Hausdorff uniform spaces. Also given are some relationships between the set of all cluster points of the Picard iterates and the set of all fixed points for the mapping. These are obtained by assuming that the latter set is nonempty and by considering certain “quasi"-contractive conditions. The ("quasi") contractive conditions are defined by using a suitable family of pseudometrics on the uniform space.