Abstract
AbstractIn this paper, some special mappings of several variables such as the multicubic and the multimixed quadratic–cubic mappings are introduced. Then, the systems of equations defining a multicubic and a multimixed quadratic–cubic mapping are unified to a single equation. Under some mild conditions, it is shown that a multimixed quadratic–cubic mapping can be multiquadratic, multicubic and multiquadratic–cubic. Furthermore, by applying a known fixed-point theorem, the Hyers–Ulam stability of multimixed quadratic–cubic, multiquadratic, multicubic and multiquadratic–cubic are studied in non-Archimedean normed spaces.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference45 articles.
1. Aczel, J., Dhombres, J.: Functional Equations in Several Variables, vol. 31. Cambridge University Press, Cambridge (1989)
2. Aoki, T.: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. 2, 64–66 (1950)
3. Bahyrycz, A., Ciepliński, K., Olko, J.: On an equation characterizing multi-additive–quadratic mappings and its Hyers–Ulam stability. Appl. Math. Comput. 265, 448–455 (2015)
4. Bahyrycz, A., Ciepliński, K., Olko, J.: On Hyers–Ulam stability of two functional equations in non-Archimedean spaces. J. Fixed Point Theory Appl. 18, 433–444 (2016)
5. Bodaghi, A.: Cubic derivations on Banach algebras. Acta Math. Vietnam. 38(4), 517–528 (2013)
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