On certain functional equation related to derivationsMarcen, Benjamin (Avtor) Vukman, Joso (Avtor) prime ringsemiprime ringderivationJordan derivationfunctional equationIn this article, we prove the following result. Let n ≥ 3 be some fixed integer and let R be a prime ring with ≠ + − char R n 1 !2n 2 ( ) ( ) . Suppose there exists an additive mapping D : R → R satisfying the relation 2n−2 D ( x n ) = ( n − 2 ∑ i = 0 ( n − 2 i ) x i D ( x 2 ) x n − 2 − i ) + ( 2 n − 2 − 1 ) ( D ( x ) x n − 1 + x n − 1 D ( x ) ) + n − 2 ∑ i = 1 ( i ∑ k = 2 ( 2 k − 1 − 1 ) ( n − k − 2 i − k ) + n − 1 − i ∑ k = 2 ( 2 k − 1 − 1 ) ( n − k − 2 n − i − k − 1 ) ) x i D ( x ) x n − 1 − i for all x ∈ R. In this case, D is a derivation. This result is related to a classical result of Herstein, which states that any Jordan derivation on a prime ring with char(R) ≠ 2 is a derivation.De Gruyter Open20242025-07-18 03:07:14Znanstveno delo93758UDK: 517.965COBISS_ID: 190231299DOI: 10.1515/math-2023-0166ISSN pri članku: 2391-5455sl