General system of cubic–quartic functional equations in quasi-β-normed spaces
- 19 June 2022
- journal article
- research article
- Published by Taylor & Francis Ltd in International Journal of General Systems
- Vol. 51 (8), 735-757
- https://doi.org/10.1080/03081079.2022.2086240
Abstract
In the current article, we define the multicubic–quartic mappings and describe them as an equation. We also study n-variable mappings, which are mixed type cubic–quartic in each variable and then give a characterization of such mappings. Indeed, we unify the general system of cubic–quartic functional equations defining a multimixed cubic–quartic mapping to a single equation, say, the multimixed cubic–quartic functional equation. Furthermore, we show under what conditions every multimixed cubic–quartic mapping can be multicubic, multiquartic and multicubic–quartic. In addition, by means of a known fixed-point result, we prove the Găvrua stability of multimixed cubic–quartic functional equations in the setting of quasi-β-normed spaces. One of the important results is that every multimixed cubic–quartic functional equation on a quasi-β-normed space is the Hyers–Ulam stable. Lastly, we investigate the hyperstability of multicubic -derivations on -algebras.
Keywords
This publication has 37 references indexed in Scilit:
- On the generalized Hyers–Ulam stability of multi-quadratic mappingsComputers & Mathematics with Applications, 2011
- Generalized stability of multi-additive mappingsApplied Mathematics Letters, 2010
- A Fixed Point Approach to the Stability of Quintic and Sextic Functional Equations in Quasi--Normed SpacesJournal of Inequalities and Applications, 2010
- On the Stability of Generalized Quartic Mappings in Quasi-β-Normed SpacesJournal of Inequalities and Applications, 2010
- Quartic functional equationsJournal of Mathematical Analysis and Applications, 2005
- The generalized Hyers–Ulam–Rassias stability of a cubic functional equationJournal of Mathematical Analysis and Applications, 2002
- A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive MappingsJournal of Mathematical Analysis and Applications, 1994
- On approximation of approximately linear mappings by linear mappingsJournal of Functional Analysis, 1982
- On the stability of the linear mapping in Banach spacesProceedings of the American Mathematical Society, 1978
- On the Stability of the linear Transformation in Banach Spaces.Journal of the Mathematical Society of Japan, 1950