Displaying similar documents to “Perturbations of isometries between Banach spaces”

A note on the Hyers-Ulam problem

Yunbai Dong (2015)

Colloquium Mathematicae

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Let X,Y be real Banach spaces and ε > 0. Suppose that f:X → Y is a surjective map satisfying | ∥f(x)-f(y)∥ - ∥x-y∥ | ≤ ε for all x,y ∈ X. Hyers and Ulam asked whether there exists an isometry U and a constant K such that ∥f(x) - Ux∥ ≤ Kε for all x ∈ X. It is well-known that the answer to the Hyers-Ulam problem is positive and K = 2 is the best possible solution with assumption f(0) = U0 = 0. In this paper, using the idea of Figiel's theorem on nonsurjective isometries, we give a new...

A Non-standard Version of the Borsuk-Ulam Theorem

Carlos Biasi, Denise de Mattos (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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E. Pannwitz showed in 1952 that for any n ≥ 2, there exist continuous maps φ:Sⁿ→ Sⁿ and f:Sⁿ→ ℝ² such that f(x) ≠ f(φ(x)) for any x∈ Sⁿ. We prove that, under certain conditions, given continuous maps ψ,φ:X→ X and f:X→ ℝ², although the existence of a point x∈ X such that f(ψ(x)) = f(φ(x)) cannot always be assured, it is possible to establish an interesting relation between the points f(φ ψ(x)), f(φ²(x)) and f(ψ²(x)) when f(φ(x)) ≠ f(ψ(x)) for any x∈ X, and a non-standard version of the...

The Hyers-Ulam-Aoki Type Stability of Some Functional Equations on Banach Lattices

Nutefe Kwami Agbeko (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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In Agbeko (2012) the Hyers-Ulam-Aoki stability problem was posed in Banach lattice environments with the addition in the Cauchy functional equation replaced by supremum. In the present note we restate the problem so that it relates not only to supremum but also to infimum and their various combinations. We then propose some sufficient conditions which guarantee its solution.

Hyers-Ulam constants of Hilbert spaces

Taneli Huuskonen, Jussi Väısälä (2002)

Studia Mathematica

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The best constant in the Hyers-Ulam theorem on isometric approximation in Hilbert spaces is equal to the Jung constant of the space.