The stability of Dhombres’ equation in Riesz spaces

One of the most important members of the class of conditional Cauchy equations with the condition dependent on the unknown function is Dhombres’ equation F ( x ) + F ( y ) ≠ 0 ⟹ F ( x + y ) = F ( x ) + F ( y ) . This paper is devoted to the stability of the above equation in the class of functions F : G → L mapping an abelian group ( G , + ) into a Riesz space L . proof, we use the Johnson–Kist Representation Theorem.