On Ulam Stability of a Linear Difference Equation in Banach Spaces

We obtain a result on Ulam stability and on the best Ulam constant for the linear difference equation x(n+2) = ax(n+1) + bx(n), where K is one of the fields R or C, a, b is an element of K and (x(n))(n >= 0) is a sequence in a Banach space X over the field K. In this way, we improve and complement some recent results on Ulam stability of the second-order linear difference equation with constant coefficients.