On a certain property and a new definition of generalized almost periodic functions of A. S. Besicovitch

1963 ◽  
pp. 131-149
Author(s):  
A. S. Kovan′ko
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Definition Of

scholarly journals Almost Periodic Functions on Time Scales and Applications

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Yongkun Li ◽  
Chao Wang
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Mathematical Methods ◽  
Variable Delays ◽  
Definition Of ◽  
Almost Periodic Time Scales

We first propose the concept of almost periodic time scales and then give the definition of almost periodic functions on almost periodic time scales, then by using the theory of calculus on time scales and some mathematical methods, some basic results about almost periodic differential equations on almost periodic time scales are established. Based on these results, a class of high-order Hopfield neural networks with variable delays are studied on almost periodic time scales, and some sufficient conditions are established for the existence and global asymptotic stability of the almost periodic solution. Finally, two examples and numerical simulations are presented to illustrate the feasibility and effectiveness of the results.

scholarly journals Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Yongkun Li ◽  
Chao Wang
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Almost Periodic Functions ◽  
Dynamic Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Periodic Sequences ◽  
Nonlinear Dynamic Equations ◽  
Definition Of

Firstly, we propose a concept of uniformly almost periodic functions on almost periodic time scales and investigate some basic properties of them. When time scaleT=ℝorℤ, our definition of the uniformly almost periodic functions is equivalent to the classical definitions of uniformly almost periodic functions and the uniformly almost periodic sequences, respectively. Then, based on these, we study the existence and uniqueness of almost periodic solutions and derive some fundamental conditions of admitting an exponential dichotomy to linear dynamic equations. Finally, as an application of our results, we study the existence of almost periodic solutions for an almost periodic nonlinear dynamic equations on time scales.

scholarly journals Almost Periodic Functions on the Quantum Time Scale and Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Yongkun Li
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Time Scale ◽  
Lyapunov Method ◽  
Almost Periodic Functions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Quantum Time ◽  
Definition Of

In this paper, we first propose two types of concepts of almost periodic functions on the quantum time scale. Secondly, we study some basic properties of almost periodic functions on the quantum time scale. Thirdly, based on these, we study the existence and uniqueness of almost periodic solutions of dynamic equations on the quantum time scale by Lyapunov method. Then, we give an equivalent definition of almost periodic functions on the quantum time scale. Finally, as an application, we propose a class of high-order Hopfield neural networks on the quantum time scale and establish the existence and global exponential stability of almost periodic solutions of this class of neural networks.

Almost periodic functions

Mathematika ◽  
1955 ◽  
Vol 2 (2) ◽  
pp. 128-131 ◽  
Author(s):  
J. D. Weston
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions
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