Journal
ACTA MATHEMATICA HUNGARICA
Volume 141, Issue 1-2, Pages 58-67Publisher
SPRINGER
DOI: 10.1007/s10474-013-0302-3
Keywords
Cauchy equation; hyperstability; cocycle; Hyers-Ulam stability
Categories
Ask authors/readers for more resources
We show that a very classical result, proved by T. Aoki, Z. Gajda and Th. M. Rassias and concerning the Hyers-Ulam stability of the Cauchy equation f(x+y)=f(x)+f(y), can be significantly improved. We also provide some immediate applications of it (among others for the cocycle equation, which is useful in characterizations of information measures). In particular, we give a solution to a problem that was formulated more than 20 years ago and concerned optimality of some estimations. The proof of that result is based on a fixed point theorem.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available