Some remarks on the absolute continuity of set-valued mappings
Journal Title: Дослідження в математиці і механіці - Year 2017, Vol 22, Issue 2
Abstract
Recently, many authors have considered the existence, uniqueness and properties of solutions of set-valued differential and integral-differential equations, higher-order equations and investigated impulsive and control systems within the framework of the theory of set-valued equations. Obviously, obtaining all these results would be impossible without the development of the theory of set-valued analysis. In particular, when considering set-valued differential equations, when the right-hand side satisfies Caratheodory conditions, absolutely continuous set-valued mappings are considered as solutions. The article show that absolutely continuous set-valued mappings (under the existing concepts of the derivative and integral) do not satisfy those properties that are satisfied by single-valued absolutely continuous functions and therefore it is proposed to introduce additionally the concept of a integrally absolutely continuous set-valued mapping.
Authors and Affiliations
T. A. Komleva, L. I. Plotnikova, A. V. Plotnikov
Keywords
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