Abstract
Let R be a semiprime ring with involution ∗ and let F, D : R → R be additive mappings satisfying the conditions (i) F(x 2) = F(x)x ∗+x ∗ D(x) and D(x 2) = D(x)x ∗+x ∗ D(x); (ii) F(x n + 1) = F(x)(x ∗)n+x ∗ D(x)(x ∗)n − 1+(x ∗)2 D(x)(x ∗)n − 2+⋯+(x ∗)n D(x) for all x ∈ R. Then, F(x y) = F(y)x ∗+y ∗ D(x) and D(x y) = D(y)x ∗+y ∗ D(x) for all x, y ∈ R.
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The authors are greatly indebted to the referee for his/her several useful suggestions and valuable comments to improve the presentation of this paper.
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Rehman, N.u., Ansari, A.Z. On Additive Mappings in a ∗-Ring with an Identity Element. Vietnam J. Math. 43, 819–828 (2015). https://doi.org/10.1007/s10013-015-0163-x
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DOI: https://doi.org/10.1007/s10013-015-0163-x