On certain functional equations related to Jordan triple $${(\theta, \phi)}$$-derivations on semiprime rings |
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Authors: | Ajda Fo?ner Joso Vukman |
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Institution: | 1.Faculty of Management,University of Primorska,Koper,Slovenia;2.Department of Mathematics and Computer Science, Faculty of Natural Sciences and Mathematics,University of Maribor,Maribor,Slovenia |
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Abstract: | The main purpose of this paper is to prove the following result. Let R be a 2-torsion free semiprime ring with symmetric Martindale ring of quotients Q s and let \({\theta}\) and \({\phi}\) be automorphisms of R. Suppose \({T:R\rightarrow R}\) is an additive mapping satisfying the relation \({T(xyx)=T(x)\theta (y)\theta (x)-\phi (x)T(y)\theta (x)+\phi (x)\phi (y)T(x)}\), for all pairs \({x,y\in R}\). In this case T is of the form \({2T(x)=q\theta (x)+\phi (x)q}\), for all \({x\in R}\) and some fixed element \({q\in Q_{s}}\). |
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