Functional identities of degree 2 in triangular rings

Let R be a triangular ring. The problem of describing the form of additive maps F1,F2,G1,G2:R→R satisfying functional identity F1(x)y+F2(y)x+xG2(y)+yG1(x)=0 for all x,y∈R is considered. As an application generalized inner biderivations and commuting additive maps of certain triangular rings are determined.