Abstract
In this article we prove the following result. Let n ≥ 1 be some fixed integer, and let R be a prime ring with 2n ≤ char(R) ≠ 2. Suppose there exists an additive mapping T: R → R satisfying the relation for all x ∈ R. In this case, T is of the form 4T(x) = qx + xq for all x ∈ R, where q is some fixed element from the symmetric Martindale ring of quotients. This result makes it possible to solve some functional equations in prime rings with involution which are related to bicircular projections.
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