On certain functional equation arising from ▫$(m, n)$▫-Jordan centralizers in prime rings
Peršin, Nina, 1981- ; Vukman, Joso
The purpose of this paper is to prove the following result. Let ▫$m \ge 1$▫, ▫$n \ge 1$▫ be some fixed integers and let ▫$R$▫ be a prime ring with ▫$\text{char}(R)= 0$▫ or ▫$(m+n)^2 < ...\text{char}(R)$▫. Suppose there exists an additive mapping ▫$T \colon R \to R$▫ satisfying the relation ▫$2(m+n)^2T(x^3) = m(2m+n)T(x)x^2 + 2mnxT(x)x + n(2n+m)x^2T(x)$▫ for all ▫$x \in R$▫. In this case ▫$T$▫ is a two-sided centralizer.
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