Caristi Type Coincidence Point Theorem in Topological Spaces

The paper is concerned with a very general version of Caristi’s coincidence theorem, in topological spaces (X, τ) satisfying some completeness conditions with respect to a function p : X ×X → [0,∞), and having as consequence Caristi’s fixed point theorem. The general result is applied to various concrete situations quasi-metric spaces, bornological spaces to obtain versions of Ekeland’s variational principle. The paper contains some interesting results, but it is written in a negligent and superficial manner, so it needs a serious revision.