We will apply the fixed point method for proving the Hyers-Ulam-Rassias stability of a Volterra integral equation of the second kind.

We prove the Hyers-Ulam stability of the generalized Fibonacci functional equationF(x)-g(x)F(h(x))=0, wheregandhare given functions.

Given a vector spaceX, we investigate the solutionsf:R→Xof the linear functional equation of third orderfx=pfx-1+qfx-2+rf(x-3), which is strongly associated with a well-known identity for the Fibonacci numbers. Moreover, we prove the Hyers-Ulam stability of that equation.