Abstract
In the present paper, inspired by methods contained in Gajda and Kominek (Stud Math 100:25–38, 1991) we generalize the well known sandwich theorem for subadditive and superadditive functionals to the case of delta-subadditive and delta-superadditive mappings. As a consequence we obtain the classical Hyers–Ulam stability result for the Cauchy functional equation. We also consider the problem of supporting delta-subadditive maps by additive ones.
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Olbryś, A. On Sandwich Theorem for Delta-Subadditive and Delta-Superadditive Mappings. Results Math 72, 385–399 (2017). https://doi.org/10.1007/s00025-016-0627-7
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DOI: https://doi.org/10.1007/s00025-016-0627-7