scholarly journals Weighted pseudo-almost periodic functions on time scales with applications to cellular neural networks with discrete delays

2016 ◽  
Author(s):  
Yongkun Li ◽  
Lili Zhao
Keyword(s):  
Neural Networks ◽  
Time Scales ◽  
Cellular Neural Networks ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Pseudo Almost Periodic Functions ◽  
Discrete Delays ◽  
Pseudo Almost Periodic

THE CONNECTION BETWEEN PSEUDO ALMOST PERIODIC FUNCTIONS DEFINED ON TIME SCALES AND ON THE REAL LINE

2017 ◽  
Vol 95 (3) ◽  
pp. 482-494 ◽  
Author(s):  
CHAO-HONG TANG ◽  
HONG-XU LI
Keyword(s):  
Time Scales ◽  
Almost Periodic Functions ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Necessary And Sufficient Condition ◽  
Periodic Functions ◽  
Pseudo Almost Periodic Functions ◽  
Necessary And Sufficient ◽  
Pseudo Almost Periodic ◽  
Uniformly Continuous

A necessary and sufficient condition for a continuous function $g$ to be almost periodic on time scales is the existence of an almost periodic function $f$ on $\mathbb{R}$ such that $f$ is an extension of $g$. Our aim is to study this question for pseudo almost periodic functions. We prove the necessity of the condition for pseudo almost periodic functions. An example is given to show that the sufficiency of the condition does not hold for pseudo almost periodic functions. Nevertheless, the sufficiency is valid for uniformly continuous pseudo almost periodic functions. As applications, we give some results on the connection between the pseudo almost periodic (or almost periodic) solutions of dynamic equations on time scales and of the corresponding differential equations.

scholarly journals Some Properties of Weighted Pseudo almost Periodic Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhe-Ming Zheng ◽  
Hui-Sheng Ding ◽  
Gaston M. N’Guérékata
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Proper Subspace ◽  
Equivalent Definition ◽  
Classical Space ◽  
Pseudo Almost Periodic Functions ◽  
Close Relationship ◽  
Pseudo Almost Periodic ◽  
Asymptotically Almost Periodic

Several interesting and new properties of weighted pseudo almost periodic functions are established. Firstly, we obtain an equivalent definition for weighted pseudo almost periodic functions, which shows a close relationship between asymptotically almost periodic functions and weighted pseudo almost periodic functions; secondly, we prove that the space of asymptotically almost periodic functions is always a proper subspace of the space of weighted pseudo almost periodic functions; thirdly, we show that under some cases, the space of weighted pseudo almost periodic functions equals the classical space of pseudo almost periodic functions.

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