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Given a finite collection of (one-valued or multivalued ) mappings between metric spaces, the problem of search and approximation of some their singularities is considered. By singularities we mean here some special subsets such as common fixed point set, coincidence set, of common preimages of a given closed subspace, set of common roots and some others. We present some new results in this area based on the use of functionals strictly subjected to convergent series, which were recently introduced by the author.