Functionals strictly subjected to convergent series and search for singularities of mappings

This paper is a continuation of the author’s previous works where the concepts of search functionals were introduced and used to develop methods of cascade search for singularities of mappings between metric spaces. Such singularities of mappings were considered as coincidences, common preimages, common fixed points and common roots of finite sets of mappings. In this paper, a new class of functionals strictly subjected to convergent series is introduced. With the help of such functionals the problems of local search for the above-mentioned singularities of mappings between metric spaces are investigated. Some new iteration schemes are suggested. Generalizations of several known results are obtained.