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Displaying similar documents to “Some surjectivity theorems with applications”

Second order evolution equations with parameter

Jan Bochenek, Teresa Winiarska (1994)

Annales Polonici Mathematici

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We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter h ∈ Ω ⊂ ℝ m . Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.

On infinite composition of affine mappings

László Máté (1999)

Fundamenta Mathematicae

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 Let F i = 1 , . . . , N be affine mappings of ℝ n . It is well known that if there exists j ≤ 1 such that for every σ 1 , . . . , σ j ∈ 1 , . . . , N the composition (1) F σ 1 ∘ . . . ∘ F σ j is a contraction, then for any infinite sequence σ 1 , σ 2 , . . . ∈ 1 , . . . , N and any z ∈ ℝ n , the sequence (2) F σ 1 ∘ . . . ∘ F σ n ( z ) is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any z ∈ ℝ n and any σ = σ 1 , σ 2 , . . . belonging to some subshift Σ of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every σ = σ 1 , σ 2 , . . . ∈ Σ the composition (1) is a contraction....