### Nina Peršin and Joso Vukman

Prušnikova 48, 2000 Maribor, Slovenia
e-mail: nina_persin@t-2.net

Department of Mathematics and Computer Science, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
e-mail: joso.vukman@uni-mb.si

Abstract.   The purpose of this paper is to prove the following result. Let m≥ 1,n≥ 1 be some fixed integers and let R be a prime ring with char(R)=0 or (m+n)2 < char (R). Suppose there exists an additive mapping T:R → R satisfying the relation 2(m+n)2T(x3)=m(2m+n)T(x)x2+2mnxT(x)x+n(2n+m)x2T(x) for all x R. In this case T is a two-sided centralizer.

2010 Mathematics Subject Classification.   16W10, 46K15, 39B05.

Key words and phrases.   Ring, prime ring, semiprime ring, Banach space, Hilbert space, algebra of all bounded linear operators, standard operator algebra, derivation, Jordan derivation, left (right) centralizer, two-sided centralizer, left (right) Jordan centralizer, (m,n)-Jordan centralizer.

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DOI: 10.3336/gm.47.1.09

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