Abstract
The exponentiation theory of linear continuous operators on Banach spaces can be extended in manifold ways to a multivalued context. In this paper we explore the Maclaurin exponentiation technique which is based on the use of a suitable power series. More precisely, we discuss about the existence and characterization of the Painlevé–Kuratowski limit
under different assumptions on the multivalued map \(F\!:X\rightrightarrows X\). In Part II of this work we study the so-called recursive exponentiation method which uses as ingredient the set of trajectories associated to a discrete time evolution system governed by \(F\).
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Cabot, A., Seeger, A. Multivalued Exponentiation Analysis. Part I: Maclaurin Exponentials. Set-Valued Anal 14, 347–379 (2006). https://doi.org/10.1007/s11228-006-0019-3
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DOI: https://doi.org/10.1007/s11228-006-0019-3