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Information × Registration Number 0221U103142, 0118U000097 , R & D reports Title Problems of nonlinear analysis for continuation of reflections belonging to different functional classes on topological and topological vector spaces popup.stage_title Head Popov Mykhailo M., Registration Date 15-02-2021 Organization Vasyl Stefanyk Precarpathian National University, State Higher Educational Institution popup.description2  Keywords: vector lattice, Banach lattice, orthogonally additive operator, Behr first class functions, fragmentary mappings, Lindelleph space, continuous fraction, branched chain fraction Object of research: topological, topological vector spaces, vector lattices, Banach lattices. The aim of the project is to solve (both new and well-known unsolved) problems of general topology and functional analysis of the continuation of different types of mappings on topological and topological vector spaces. Research methodology. Both well-known approaches and methods are used to solve the problems (classical Titze theorem, nonlinear Hahn-Banach theorem, Kantorovich's theorem on the continuation of positive operators) and new ones are created. One of the new approaches is based on the concept of fragmentary mapping. To establish the possibility of continuing the functions of the first Behr class from a subspace to the whole space that satisfies the conditions of the compactness type, we must first investigate the properties of the functions of the first Behr class over the whole space and establish their functional countable fragmentation. Then, taking into account the hereditary nature of fragmentation, the necessary condition for the continuing functions defined in the subspace is obtained. In particular, it makes it possible to obtain general results on the continuation of the functions of the first class of Behr and indicates the idea of building counterexamples to the problems of this topic. Another new method for studying problems on the continuation of mappings is based on the construction of abstract Gaar systems on vector lattices. The idea of the method is that in the presence of an abstract Gaar system on the sublattice, which is the unconditional ordinal basis of this sublattice, the desired continuation of the ordinal continuous mapping given on this sublattice is constructed as the corresponding ordinal sum of the Fourier series. Product Description popup.authors Dmytryshyn Roman I. Karlova Olena O. Mykhailiuk Volodymyr V. Nykyforchyn Oleg R. popup.nrat_date 2021-02-15 Close