On Ulam stability of a third order linear difference equation in Banach spaces

Abstract

We obtain a result on Ulam stability and on the best Ulam constant for the linear difference equation $$x_{n+3}=ax_{n+2}+bx_{n+1}+c x_n,$$ $$a,b,c \in \mathbb {K}$$ , where $$\mathbb {K}$$ is one of the fields $$\mathbb {R}$$ or $$\mathbb {C},$$ and $$(x_n)_{n\ge 0}$$ is a sequence in a Banach space X over the field $$\mathbb {K}$$ .