A note on S-asymptotically periodic functions

Abstract In [Haiyin Gao, Ke Wang, Fengying Wei, Xiaohua Ding, Massera-type theorem and asymptotically periodic Logistic equations, Nonlinear Analysis: Real World Applications 7 (2006) 1268–1283, Lemma 2.1] it is established that a scalar S -asymptotically ω -periodic function (that is, a continuous and bounded function f : [ 0 , ∞ ) → R such that lim t → ∞ ( f ( t + ω ) − f ( t ) ) = 0 ) is asymptotically ω -periodic. In this note we give two examples to show that this assertion is false.