Abstract
Here we follow the notation of Chap. 5, and denote the pseudomodular from Definition 5.1.1 more precisely by \(w_{\lambda }^{\mathbb{N}}(x,y)\). For I = [a, b] and a metric space (M, d), we define new pseudomodulars on the set X = M I, whose induced modular spaces consist of mappings of bounded generalized variation (in the sense of Jordan, Wiener-Young, Riesz-Medvedev). We prove the Lipschitz continuity of a superposition operator (of “multiplication”) and establish the existence of selections of bounded variation of compact-valued BV multifunctions. An application to ordinary differential equations in Banach spaces is also given.
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Chistyakov, V.V. (2015). Mappings of Bounded Generalized Variation. In: Metric Modular Spaces . SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-25283-4_6
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