Contractions of Banach, Tarafdar, Meir–Keeler, Ćirić–Jachymski–Matkowski and Suzuki types and fixed points in uniform spaces with generalized pseudodistances

In the uniform spaces (sequentially complete and not sequentially complete), we introduce the concept of the JJ-families of generalized pseudodistances, we apply it to construct JJ-generalized contractions and we provide the conditions guaranteeing the existence and uniqueness of fixed points of these contractions and the convergence to these fixed points of each iterative sequence of these contractions. Our JJ-generalized contractions essentially extend Banach, Tarafdar, Meir–Keeler, Ćirić–Jachymski–Matkowski and Suzuki contractions to uniform spaces with JJ-families of generalized pseudodistances. Examples showing a difference between our results and the well-known ones are given. The definitions, the results and the method to investigate uniqueness and iterative approximation of fixed points of the maps presented here are new for maps in uniform and locally convex spaces and even in metric spaces.