We prove that a main result of T. Suzuki [J. Math. Anal. Appl. 253 (2001), 440-458, Theorem 1, p. 451] has been for the first time proved 20 years ago by Tasković [Proc. Amer. Math. Soc. 94 (1985), 427-432, Theorem 2, p. 430], and second time proved by Tasković [Math. Japonica, 35 (1990), 645-666, Theorem 2, p. 654] as a very special case of the so-called Localization Monotone Principle.