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A note on \(S\)-asymptotically periodic functions. (English) Zbl 1163.42305

Summary: H. Gao, K. Wang, F. Wei and X. Ding [Nonlinear Anal., Real World Appl. 7, No. 5, 1268–1283 (2006; Zbl 1162.34325)] established that a scalar \(S\)-asymptotically \(\omega \)-periodic function (that is, a continuous and bounded function \(f:[0,\infty ]\to \mathbb R\) such that lim\(_{t\rightarrow \infty} (f(t+\omega ) - f(t))=0)\) is asymptotically \(\omega \)-periodic. In this note we give two examples to show that this assertion is false.

MSC:

42A75 Classical almost periodic functions, mean periodic functions

Citations:

Zbl 1162.34325
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References:

[1] Gao, Haiyin; Wang, Ke; Wei, Fengying; Ding, Xiaohua, Massera-type theorem and asymptotically periodic logistic equations, Nonlinear Analysis: Real World Applications, 7, 1268-1283 (2006) · Zbl 1162.34325
[2] C. Corduneanu, Almost Periodic Functions, second edition, Chelsea, New York, 1989; C. Corduneanu, Almost Periodic Functions, second edition, Chelsea, New York, 1989 · Zbl 0672.42008
[3] Zaidman, S., (Almost-Periodic Functions in Abstract Spaces. Almost-Periodic Functions in Abstract Spaces, Res. Notes in Math., vol. 126 (1985), Pitman: Pitman Boston, MA) · Zbl 0648.42006
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