Abstract
The purpose of the present work is to obtain some results concerning approximate n-Jordan homomorphisms on Banach algebras. The results of this paper correct and improve the main results from Ghaleh and Ghasemi (Bull Iran Math Soc 39:347–353, 2013) and improve some results obtained in Gordji et al. (J Ineq Appl 870843, 2009), Miura et al. (J Ineq Appl 2005(4):435–441, 2005). Applications in connection with classical results are also provided.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
An, G.: Characterizations of \(n\)-Jordan homomorphisms. Linear Multilinear Algebra 66, 671–680 (2018)
Badora, R.: On approximate ring homomorphisms. J. Math. Anal. Appl. 276, 589–597 (2002)
Badora, R., Przebieracz, B.: On approximate group homomorphisms. J. Math. Anal. Appl. 462, 505–520 (2018)
Bodaghi, A., Shojaee, B.: \(n\)-Jordan homomorphisms on \(C^*\)-algebras. J. Linear Topol. Algebra 1, 1–7 (2012)
Bodaghi, A., İnceboz, H.: \(n\)-Jordan homomorphisms on commutative algebras. Acta Math. Univ. Comenianae LXXXVI I, 141–146 (2018)
Brzdȩk, J.: Hyperstability of the Cauchy equation on restricted domains. Acta Math. Hungarica 141, 58–67 (2013)
Brzdȩk, J., Ciepliński, K.: Hyperstability and superstability. Abstr. Appl. Anal. 401756, (2013)
Brzdȩk, J., Fos̆ner, A.: Remarks on the stability of Lie homomorphisms. J. Math. Anal. Appl. 400, 585–596 (2013)
Brzdȩk, J., Popa, D., Raşa, I., Xu, B.: Ulam Stability of Operators. Academic Press, Elsevier, Oxford (2018)
Czerwik, S.: On the stability of the quadratic mapping in normed spaces. Abh. Math. Sem. Hamburg 62, 59–64 (1992)
Ghaleh, S.G., Ghasemi, K.: Hyers-Ulam-Rassias stability of \(n\)-Jordan \(*\)-homomorphisms on \(C^*\)-algebras. Bull. Iran. Math. Soc. 39, 347–353 (2013)
Gordji, M.E.: \(n\)-Jordan homomorphisms. Bull. Austral. Math. Soc. 80, 159–164 (2009)
Gordji, M.E., Jabbari, A., Kapapinar, E.: Automatic continuity of surjective \(n\)-homomorphisms on Banach algebras. Bull. Iran. Math. Soc. 41, 1207–1211 (2015)
Gordji, M.E., Karimi, T., Gharetapeh, S.K.: Approximately \(n\)-Jordan homomorphisms on Banach algebras. J. Ineq. Appl. 870843, (2009)
Hejazian, Sh, Mirzavaziri, M., Moslehian, M.S.: \(n\)-homomorphisms. Bull. Iran. Math. Soc. 31, 13–23 (2005)
Herstein, I.N.: Jordan homomorphisms. Trans. Amer. Math. Soc. 81, 331–341 (1956)
Honary, T.G., Shayanpour, H.: Automatic continuity of \(n\)-homomorphisms between Banach algebras. Quaest. Math. 33, 189–196 (2010)
Miura, T., Takahasi, S.E., Hirasawa, G.: Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras. J. Ineq. Appl. 2005(4), 435–441 (2005)
Park, C., Rassias, MTh: Additive functional equations and partial multipliers in C*-algebras. RACSAM 113, 2175–2188 (2019)
Park, C., Rassias, ThM: Homomorphisms and derivations in proper JCQ*-triples. J. Math. Anal. Appl. 337, 1404–1414 (2008)
Park, E., Trout, J.: On the nonexistence of nontrivial involutive \(n\)-homomorphisms of \(C^*\)-algebras. Trans. Amer. Math. Soc. 361, 1949–1961 (2009)
Rassias, ThM: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72, 297–300 (1978)
Zelazko, W.: A characterization of multiplicative linear functionals in complex Banach algebras. Studia Math. 30, 83–85 (1968)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Khodaei, H. Asymptotic Behavior of n-Jordan Homomorphisms. Mediterr. J. Math. 17, 143 (2020). https://doi.org/10.1007/s00009-020-01580-w
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00009-020-01580-w