Common fixed point theorems and variational principle in generating spaces of quasi-metric family

Abstract

In this paper, we introduce the concept of order relation in generating spaces of quasi-metric family and establish common fixed point theorems for set-valued mappings in this spaces. As consequences, we also give the variational principle, fixed point theorems for single-valued and set-valued mappings and equivalence between them in complete generating spaces of quasi-metric family. Some applications of these results to fuzzy metric spaces in sense of Kaleva and Seikkala (1984) and probabilistic metric spaces are presented.