Szczegóły publikacji
Opis bibliograficzny
On stability and hyperstability of an equation characterizing multi-Cauchy-Jensen mappings / Anna BAHYRYCZ, Jolanta OLKO // Results in Mathematics ; ISSN 1422-6383. — 2018 — vol. 73 iss. 2 art. no. 55, s. 1–18. — Bibliogr. s. 16–18, Abstr. — Publikacja dostępna online od: 2018-03-19
Autorzy (2)
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 117088 |
|---|---|
| Data dodania do BaDAP | 2018-10-12 |
| Tekst źródłowy | URL |
| DOI | 10.1007/s00025-018-0815-8 |
| Rok publikacji | 2018 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Results in Mathematics |
Abstract
Recently, functions of several variables satisfying, with respect to each variable, some functional equation (among them Cauchy's, Jensen's, quadratic and other ones) have been studied. We give a new characterization of multi-Cauchy-Jensen mappings, which states that a function fulfilling some equation on a restricted domain is multi-Cauchy-Jensen. Next, using a fixed point theorem, it is proved that a function which approximately satisfies (on restricted domain) the equation characterizing such functions is close (in some sense) to the solution of the equation. This result is a tool for obtaining a generalized Hyers-Ulam stability or hyperstability of this equation for particular control functions, which is presented in several examples.
