On Sandwich Theorem for Delta-Subadditive and Delta-Superadditive Mappings

On Sandwich Theorem for Delta-Subadditive and Delta-Superadditive Mappings 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Results in Mathematics Springer Journals

On Sandwich Theorem for Delta-Subadditive and Delta-Superadditive Mappings

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Publisher
Springer International Publishing
Copyright
Copyright © 2016 by The Author(s)
Subject
Mathematics; Mathematics, general
ISSN
1422-6383
eISSN
1420-9012
D.O.I.
10.1007/s00025-016-0627-7
Publisher site
See Article on Publisher Site

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.

Journal

Results in MathematicsSpringer Journals

Published: Dec 5, 2016

References

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