Hyers-Ulam stability of the nonlinear iterative functional equation \(G(f^{n_1}(x), \dots, f^{n_k}(x)) =F(x)\) is considered. \(F\) is assumed to be given and \(f\) an unknown function. Both \(F\) and \(f\) are self-maps of \(I\), a subset of a Banach space; \(G:I^k\to I\), where, as usual, \(I^k=I\times \cdots\times I\), \(f^0(x)=x\), \(f^{i+1}(x) =f(f^i(x))\) for \(i>0\). Also, \(n_1,\dots, n_k\) are positive integers for \(i=1,\dots, k\). By constructing a suitable uniformly convergent sequence of functions, it is established that the functional equation has a unique solution near its approximate solution.