Displaying similar documents to “Further remarks on the Nemitskii operator in Hölder spaces”

Generalized weak peripheral multiplicativity in algebras of Lipschitz functions

Antonio Jiménez-Vargas, Kristopher Lee, Aaron Luttman, Moisés Villegas-Vallecillos (2013)

Open Mathematics

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Let (X, d X) and (Y,d Y) be pointed compact metric spaces with distinguished base points e X and e Y. The Banach algebra of all 𝕂 -valued Lipschitz functions on X - where 𝕂 is either‒or ℝ - that map the base point e X to 0 is denoted by Lip0(X). The peripheral range of a function f ∈ Lip0(X) is the set Ranµ(f) = f(x): |f(x)| = ‖f‖∞ of range values of maximum modulus. We prove that if T 1, T 2: Lip0(X) → Lip0(Y) and S 1, S 2: Lip0(X) → Lip0(X) are surjective mappings such that R a n π ( T 1 ( f ) T 2 ( g ) ) ∩ R a n π ( S 1 ( f ) S 2 ( g ) ) ≠ ∅ for all...

Nonuniqueness results for ordinary differential equations

Josef Kalas (1998)

Czechoslovak Mathematical Journal

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In the present paper we give general nonuniqueness results which cover most of the known nonuniqueness criteria. In particular, we obtain a generalization of the nonuniqueness theorem of Chr. Nowak, of Samimi’s nonuniqueness theorem and of Stettner’s nonuniqueness criterion.