### On common fixed points of pairs of a single and a multivalued coincidentally commuting mappings in $D$-metric spaces.

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In this paper, we establish a new version of Siegel's fixed point theorem in generating spaces of quasi-metric family. As consequences, we obtain general versions of the Downing-Kirk's fixed point and Caristi's fixed point theorem in the same spaces. Some applications of these results to fuzzy metric spaces and probabilistic metric spaces are presented.

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