By following the approaches of Kada eet al.13, we define afamily of weak quasi-metrics in a generating space of quasimetricfamily. By using a family of weak quasi-metrics, we prove aTakahashi-type minimization theorem, a generalized Ekelandvariational principle and a general Caristi-type fixed point theoremfor set-valued maps in complete generating spaces of quasi-metricfamily. Also, by following the approach of Aubin 11, we proveanother fixed point theorem for set-valued maps in completegenerating spaces of quasi-metric family without the assumption ofowe semicontinuity. From our results in complete generating spaces ofquasi-metric family, we obtain the corresponding theorems forset-valued maps in complete fuzzy metric spaces.
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