It is well-known that the Ulam stability in locally convex cones originated from the research paper [29]. The theory of locally convex cones uses an order theoretical concept or a convex quasi-uniform structure to introduce a topological structure on a cone. In this paper, we consider the stability analysis in locally convex cones (LCC), and prove the stability of a generalized Cauchy-Jensen equation in LCC. As classical consequences, we derive the stability of the linear operator, the Cauchy-Jensen equation in LCC and the Hyers type stability of the generalized Cauchy-Jensen equation.
