Uniformly continuous superposition operators in the Banach space of Hölder functions

DOI10.1016/j.jmaa.2009.05.020zbMath1173.47043OpenAlexW1974705282MaRDI QIDQ2272023

Janusz Matkowski

Publication date: 5 August 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.05.020

zbMATH Keywords

superposition operatorHölder functionsuniform continuity of operators

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Lipschitz (Hölder) classes (26A16)

Related Items (8)

Locally defined operators in Hölder's spaces ⋮ Uniformly continuous composition operators in the space of functions of \(\varphi \)-variation with weight in the sense of Riesz ⋮ Uniformly bounded composition operators in the Banach space of bounded \((p, k)\)-variation in the sense of Riesz-Popoviciu ⋮ On uniformly continuous Nemytskij operators generated by set-valued functions ⋮ Numerical Dynamics of Integrodifference Equations: Hierarchies of Invariant Bundles in L^p (Ω) ⋮ Uniformly bounded Nemytskij operators between the Banach spaces of functions of bounded \(n\)-th variation ⋮ Uniformly bounded set-valued Nemytskij operators acting between generalized Hölder function spaces ⋮ Urysohn and Hammerstein operators on Hölder spaces

Cites Work

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• An application of B. N. Sadovskij's fixed point principle to nonlinear singular equations
• On a Characterization of Lipschitzian Operators of Substitution in the SpaceBV{a, b)
• Lipschitzian composition operators in some function spaces

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