## Stability of $$n$$-Jordan homomorphisms from a normed algebra to a Banach algebra.(English)Zbl 1470.39054

Summary: We establish the hyperstability of $$n$$-Jordan homomorphisms from a normed algebra to a Banach algebra, and also we show that an $$n$$-Jordan homomorphism between two commutative Banach algebras is an $$n$$-ring homomorphism.

### MSC:

 39B52 Functional equations for functions with more general domains and/or ranges
Full Text:

### References:

 [1] Gordji, M. E.; Karimi, T.; Gharetapeh, S. K., Approximately n-Jordan Homomorphisms on Banach algebras, Journal of Inequalities and Applications, 2009, (2009) · Zbl 1162.39017 [2] Ulam, S. M., Problems in Modern Mathematics, (1964), New York, NY, USA: John Wiley & Sons, New York, NY, USA · Zbl 0137.24201 [3] Bourgin, D. G., Approximately isometric and multiplicative transformations on continuous function rings, Duke Mathematical Journal, 16, 385-397, (1949) · Zbl 0033.37702 [4] Badora, R., On approximate derivations, Mathematical Inequalities & Applications, 9, 1, 167-173, (2006) · Zbl 1093.39024 [5] Brillouët-Belluot, N.; Brzdęk, J.; Ciepliński, K., On some recent developments in Ulam’s type stability, Abstract and Applied Analysis, 2012, (2012) · Zbl 1259.39019 [6] Maksa, G.; Páles, Z., Hyperstability of a class of linear functional equations, Acta Mathematica, 17, 2, 107-112, (2001) · Zbl 1004.39022 [7] Brzdek, J., Hyperstability of the Cauchy equation on restricted domains, Acta Mathematica Hungarica, (2013) · Zbl 1313.39037 [8] Piszczek, M., Remark on hyperstability of the general linear equation, Aequationes Mathematicae, (2013) · Zbl 1304.39033 [9] Lee, Y.-H.; Jun, K.-W., A generalization of the Hyers-Ulam-Rassias stability of the Pexider equation, Journal of Mathematical Analysis and Applications, 246, 2, 627-638, (2000) · Zbl 0957.39008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.