Retracted: Approximation of Jordan homomorphisms in Jordan-Banach algebras. (English) Zbl 1271.39024
Math. Sci., Springer 6, Paper No. 55, 5 p. (2012); retraction ibid. 9, No. 1, 57 (2015).
Editorial remark: This paper is identical with the paper [“Approximation of Jordan homomorphisms in Jordan Banach algebras”, Iran. J. Math. Sci. Inform. 8, No. 1, 39–47 (2013; Zbl 1359.39017)] by the same authors.
Summary: Using the direct method based on the Hyers-Ulam-Rassias stability, we investigate and prove the Hyers-Ulam stability of Jordan homomorphisms in Jordan-Banach algebras for the functional equation \[ \sum_ {k=2}^{n} \sum_{i_1=2}^{k}\sum _{i_2=i_1+1}^{k+1} \dots \sum_{i_n-k+1=i_{n-k}+1}^{n}f\left(\sum_{i=1,i\neq i_1,\dots, i_{n-k+1}}^{n}x_i-\sum_{r=1}^{n-k+1}x_{i _r}\right)+f\left(\sum_{i=1}^{n}x_i\right) -2^{n-1}f \left(x_1\right)=0, \] where \(n\) is an integer greater than 1.
Summary: Using the direct method based on the Hyers-Ulam-Rassias stability, we investigate and prove the Hyers-Ulam stability of Jordan homomorphisms in Jordan-Banach algebras for the functional equation \[ \sum_ {k=2}^{n} \sum_{i_1=2}^{k}\sum _{i_2=i_1+1}^{k+1} \dots \sum_{i_n-k+1=i_{n-k}+1}^{n}f\left(\sum_{i=1,i\neq i_1,\dots, i_{n-k+1}}^{n}x_i-\sum_{r=1}^{n-k+1}x_{i _r}\right)+f\left(\sum_{i=1}^{n}x_i\right) -2^{n-1}f \left(x_1\right)=0, \] where \(n\) is an integer greater than 1.
MSC:
| 39B82 | Stability, separation, extension, and related topics for functional equations |
| 39B52 | Functional equations for functions with more general domains and/or ranges |
Citations:
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