On some functional equations arising from (m, n)-Jordan derivations and commutativity of prime ringsFošner, Maja (Avtor) Vukman, Joso (Avtor) matematikaprakolobarpolprakolobarodvajanjejordansko odvajanjelevo odvajanjemathematicsprime ringsemiprime ringderivationJordan derivationleft dderivationleft Jordan derivation(mn)-Jordan drivationThe purpose of this paper is to prove the following result. Let ▫$m, n ge 1$▫ be some fixed integers with ▫$m ne n$▫, and let ▫$R$▫ be a prime ring with ▫$(m+n)^2 < text{char} (R)$▫. Suppose a nonzero additive mapping ▫$D : R to R$▫ exists satisfying the relation ▫$(m+n)^2 D(x^3) = m(3m+n) D(x)x^2 + 4mnxD(x)x + n(3n+m)x^2 D(x)$▫ for all ▫$x in R$▫. In this case ▫$D$▫ is a derivation and ▫$R$▫ is commutative.20122015-07-10 15:35:26Delo ni kategorizirano52026sl