Characterization of some non-additive mixed biskew Jordan type derivations on +-rings

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 I_1 and standard operator algebras.