For a triangular operator A : X × Y → X × Y, A = (B;C), where B : X → X and C : X ×Y → Y we study in which conditions on operators B : X → X and C : X ×Y → Y we have that: (1) the fixed point problem for triangular operator A = (B;C) is well posed (2) the operator A = (B,C) has the Ostrowski property (3) the fixed point equation (x, y) = A(x, y) is generalized Ulam-Hyers stable.