Ulam stability of a successive approximation equation (Q2182847)

Let \(X\) be a Banach space and \(T:X \to X\) a bounded linear operator. The linear difference equation \(x_{n+1} = T x_n + a_n\) associated with an iterative process for the classical linear equation \(x-T x = y\) is considered. The authors investigate the Ulam stability for a finite-dimensional space \(X\) and a Fredholm operator \(T\).