A note on ``Stability and periodicity in dynamic delay equationsʹʹ [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 Ad var, 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 D on the delay function.