Abstract
It is shown that two real functionsf andg, defined on a real intervalI, satisfy the inequalitiesf(λx + (1 − λ)y) ≤ λg(x) + (1 − λ)g(y) andg(λx + (1 − λ)y) ≥ λf(x) + (1 − λ)f(y) for allx, y ∈ I andλ ∈ [0, 1], iff there exists an affine functionh: I → ℝ such thatf ≤ h ≤ g. As a consequence we obtain a stability result of Hyers—Ulam type for affine functions.
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Nikodem, K., Wasowicz, S. A sandwich theorem and Hyers—Ulam stability of affine functions. Aeq. Math. 49, 160–164 (1995). https://doi.org/10.1007/BF01827935
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DOI: https://doi.org/10.1007/BF01827935