A characterization of quadratic-multiplicative mappings (Q652543)

Let \(P\) be a commutative unitary ring uniquely divisible by \(2\), and \(R\) be a commutative ring with no zero divisors. In this paper, the author investigates the functional equation \[ af(xy)+bf(x)f(y)+cf(x+y)+df(x-y)+k(f(x)+f(y))=0, \] where \(f:P\to R\) is the unknown function, \(a, b, c, d, k\) are elements in \(R\). This was motivated by some earlier results of Dhombres, Ger and Reich.