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On stability of a general bilinear functional equation
Authors:
- Anna Bahyrycz,
- Justyna Sikorska
Abstract
We prove the Hyers-Ulam stability of the functional equation f(a(1)x(1) + a(2)x(2), b(1)y(1) + b(2)y(2)) = C(1)f(x(1), y(1)) (*) + C(2)f(x(1), y(2)) + C(3)f(x(2), y(1)) + C(4)f(x(2), y(2)) in the class of functions from a real or complex linear space into a Banach space over the same field. We also study, using the fixed point method, the generalized stability of (*) in the same class of functions. Our results generalize some known outcomes.
- Record ID
- USL90b870097d5640f38830e18756d6f808
- Author
- Journal series
- Results in Mathematics, ISSN 1422-6383, e-ISSN 1420-9012
- Issue year
- 2021
- Vol
- 76
- No
- 3
- Pages
- 1-17
- Publication size in sheets
- 0.80
- Article number
- 143
- Keywords in English
- Hyers–Ulam stability, Generalized stability, Functional equation, Fixed point, Nonlinear operator, Linear operator
- ASJC Classification
- ;
- DOI
- DOI:10.1007/s00025-021-01447-w Opening in a new tab
- Handle.net URL
- hdl.handle.net/20.500.12128/20632 Opening in a new tab
- URL
- http://hdl.handle.net/20.500.12128/20632 Opening in a new tab
- Language
- eng (en) English
- License
- File
-
- File: 1
- On stability of a general bilinear functional equation, File Bahyrycz_Sikorska_on_stability_of_a_general.pdf / 588 KB
- Bahyrycz_Sikorska_on_stability_of_a_general.pdf
- publication date: 09-11-2023
- On stability of a general bilinear functional equation, File Bahyrycz_Sikorska_on_stability_of_a_general.pdf / 588 KB
-
- Score (nominal)
- 100
- Score source
- journalList
- Score
- = 100.0, 20-12-2023, ArticleFromJournal
- Publication indicators
- Uniform Resource Identifier
- https://opus.us.edu.pl/info/article/USL90b870097d5640f38830e18756d6f808/
- URN
urn:uni-kat-prod:USL90b870097d5640f38830e18756d6f808
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.