Remarks on hyperstability of the Cauchy functional equation

By Janusz Brzdek. 2013

71 citations recorded by the source corpus.

We present some simple observations on hyperstability for the Cauchy equation on a restricted domain. Namely, we show that (under some weak natural assumptions) functions that satisfy the equation approximately (in some sense), must be actually solutions to it. In this way we demonstrate in particular that hyperstability is not a very exceptional phenomenon as it has been considered so far. We also provide some simple examples of applications of those results.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bd97af2568bee50bac87d12326ac2faf0a0b9cf0

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In Applied Mathematics

1. Janusz Brzdek
2. Krzysztof Cieplinski
3. Liviu Cadariu
4. Justyna Sikorska
5. Wlodzimierz Fechner
6. Mohammad Sal Moslehian

In Mathematical Physics

1. Krzysztof Cieplinski
2. Janusz Brzdek
3. Liviu Cadariu

Citations in the corpus

• Fixed Point Theory and the Ulam Stability (2014, background): “Rassias concerning optimality of estimations in Theorem 29) and in [69] (in proving stability of the equation ofp-Wright affine functions); in particular, it has been discovered in this way in [49] that the property of hyperstability for the additive Cauchy equation appears quite often in a natural ”
• Hyperstability and Superstability (2013, background): “(24) Now, we are in a position to present another result from [25].”