Let F be a 2-torsion free +-ring having a unital element and a non-trivial symmetric idempotent. In the present paper, we demonstrate that, under certain mild conditions, if a map Ψ: F → F (not necessarily additive) satisfies Ψ (U♢K ◦ L) = Ψ (U) ♢K ◦ L + U♢Ψ (K) ◦ L + U♢K ◦ Ψ (L) for all U, K, L ∈ F, then Ψ is an additive +-derivation. Particularly, we apply our main result to certain special classes of +-algebras such as prime +-algebra, von Neumann algebras with no central summands of type I₁ and standard operator algebras.
Bhat et al. (Wed,) studied this question.