Minimization theorems and fixed point theorems in generating spaces of quasi-metric family

摘要

By following the approaches of Kada eet al.[13], we define a family of weak quasi-metrics in a generating space of quasimetric family. By using a family of weak quasi-metrics, we prove a Takahashi-type minimization theorem, a generalized Ekeland variational principle and a general Caristi-type fixed point theorem for set-valued maps in complete generating spaces of quasi-metric family. Also, by following the approach of Aubin [11], we prove another fixed point theorem for set-valued maps in complete generating spaces of quasi-metric family without the assumption of owe semicontinuity. From our results in complete generating spaces of quasi-metric family, we obtain the corresponding theorems for set-valued maps in complete fuzzy metric spaces.