A note on “Stability and periodicity in dynamic delay equations” [Comput. Math. Appl. 58 (2009) 264–273]

The purpose of this note is twofold: First we highlight the importance of an implicit assumption in [Murat Adıvar, Youssef N. Raffoul, Stability and periodicity in dynamic delay equations, Computers and Mathematics with Applications 58 (2009) 264–272]. Second we emphasize one consequence of the bijectivity assumption which enables ruling out the commutativity condition δ∘σ=σ∘δδ∘σ=σ∘δ on the delay function.