We analyse the composite functional equation $$f(x+2f(y))=f(x)+y+f(y)$$f(x+2f(y))=f(x)+y+f(y) on certain groups. In particular we give a description of solutions on abelian 3-groups and finitely generated free abelian groups. This is motivated… Click to show full abstract
We analyse the composite functional equation $$f(x+2f(y))=f(x)+y+f(y)$$f(x+2f(y))=f(x)+y+f(y) on certain groups. In particular we give a description of solutions on abelian 3-groups and finitely generated free abelian groups. This is motivated by a work of Pál Burai, Attila Házy and Tibor Juhász, who described the solutions of the equation on uniquely 3-divisible abelian groups.
               
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