Caristi Type Coincidence Point Theorem in Topological Spaces

A generalized Caristi type coincidence point theorem and its equivalences in the setting of topological spaces by using a kind of nonmetric type function are obtained. These results are used to establish variational principle and its equivalences in -complete spaces, bornological vector space, seven kinds of completed quasi-semimetric spaces equipped with -functions, uniform spaces with -distance, generating spaces of quasimetric family, and fuzzy metric spaces.