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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
