Generalized Hyers-Ulam-Rassias theorem in Menger probabilistic normed spaces.
Gordji, M.Eshaghi, Ghaemi, M.B., Majani, H. (2010)
Discrete Dynamics in Nature and Society
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Gordji, M.Eshaghi, Ghaemi, M.B., Majani, H. (2010)
Discrete Dynamics in Nature and Society
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Roh, Jaiok, Chang, Ick-Soon (2008)
Abstract and Applied Analysis
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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...
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