Abstract
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 ind-complete spaces, bornological vector space, seven kinds of completed quasi-semimetric spaces equipped withQ-functions, uniform spaces withq-distance, generating spaces of quasimetric family, and fuzzy metric spaces.
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