LAUSR

Abstract In the paper a general and compact fixed point theorem for dislocated (or partial) metric spaces is proved in a simple way. It appears that the reasoning is sufficiently general to spread over the well known (and complicated) classical results. In consequence, the extensions of some celebrated fixed point theorems are obtained, while their proofs are short and consistent, which is the main aim of the paper. The more sophisticated results are contained in sections devoted to cyclic mappings, common fixed points, and dislocated quasi-metric spaces. Maybe the most exciting result is presented in the final corollary; this effective criterion for Cauchy sequences can make the life of many analysts bearable.