On a factorization of mappings with a prescribed behaviour of the Cauchy difference

Roman Ger

Published: 1994-09-30

Vol. 8 (1994)

On a factorization of mappings with a prescribed behaviour of the Cauchy difference

Roman Ger

Abstract

We deal with functional congruences of the form
f(x+y) - f(x) - f(y) ∈ U + V
where U and V are given sets subjected to satisfy some "separability" conditions essentially weaker than that occurring in [4] which proved to be pretty useful especially while investigating various types of Hyers-Ulam stability problems. The goal is to factorize f into a sum of two functions whose Cauchy differences remain in U and V, respectively, or, at least to obtain an approximation of f by such a sum. An application of the newly established result in that spirit is given. Moreover, a stability result for the celebrated cocycle equation is presented and, finally, the behaviour of mappings whose Cauchy differences fall into a given Hamel basis is described.

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Ger, R. (1994). On a factorization of mappings with a prescribed behaviour of the Cauchy difference. Annales Mathematicae Silesianae, 8, 141–155. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14226

References

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Vol. 8 (1994)
Published: 1994-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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