Periodicity, almost periodicity for time scales and related functions

Chao Wang; Ravi P. Agarwal; Donal O’Regan

Nonautonomous Dynamical Systems (2016)

  • Volume: 3, Issue: 1, page 24-41
  • ISSN: 2353-0626

Abstract

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In this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.

How to cite

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Chao Wang, Ravi P. Agarwal, and Donal O’Regan. "Periodicity, almost periodicity for time scales and related functions." Nonautonomous Dynamical Systems 3.1 (2016): 24-41. <http://eudml.org/doc/281258>.

@article{ChaoWang2016,
abstract = {In this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.},
author = {Chao Wang, Ravi P. Agarwal, Donal O’Regan},
journal = {Nonautonomous Dynamical Systems},
keywords = {Time scales; Almost periodic time scales; Changing periodic time scales; time scales; almost periodic time scales; changing periodic time scales},
language = {eng},
number = {1},
pages = {24-41},
title = {Periodicity, almost periodicity for time scales and related functions},
url = {http://eudml.org/doc/281258},
volume = {3},
year = {2016},
}

TY - JOUR
AU - Chao Wang
AU - Ravi P. Agarwal
AU - Donal O’Regan
TI - Periodicity, almost periodicity for time scales and related functions
JO - Nonautonomous Dynamical Systems
PY - 2016
VL - 3
IS - 1
SP - 24
EP - 41
AB - In this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.
LA - eng
KW - Time scales; Almost periodic time scales; Changing periodic time scales; time scales; almost periodic time scales; changing periodic time scales
UR - http://eudml.org/doc/281258
ER -

References

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  1. [1] M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser Boston Inc., Boston, 2001.  Zbl0978.39001
  2. [2] C.Wang, R.P. Agarwal, Changing-periodic time scales and decomposition theorems of time scales with applications to functions with local almost periodicity and automorphy, Adv. Differ. Equ., 296 (2015) 1-21. [WoS][Crossref] 
  3. [3] C. Wang, Almost periodic solutions of impulsive BAM neural networks with variable delays on time scales, Commun. Nonlinear Sci. Numer. Simulat., 19 (2014) 2828-2842. [WoS] 
  4. [4] C. Wang, R.P. Agarwal, A classification of time scales and analysis of the general delays on time scales with applications, Math. Meth. Appl. Sci., 39 (2016) 1568-1590. [WoS] Zbl1342.26066
  5. [5] C. Wang, R.P. Agarwal, Uniformly rd-piecewise almost periodic functions with applications to the analysis of impulsive ∆- dynamic system on time scales, Appl. Math. Comput., 259 (2015) 271-292. [WoS] 
  6. [6] C. Wang, R.P. Agarwal, A further study of almost periodic time scales with some notes and applications, Abstr. Appl. Anal., (2014) 1-11 (Article ID 267384). [WoS] 
  7. [7] E.R. Kaufmann, Y.N. Raffoul, Periodic solutions for a neutral nonlinear dynamical equation on a time scale, J. Math. Anal. Appl., 319 (2006) 315-325.  Zbl1096.34057
  8. [8] Y. Li, C.Wang, Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales, Abstr. Appl. Anal., (2011). 22p (Article ID 341520).  Zbl1223.34125
  9. [9] M. Adıvar, A new periodicity concept for time scales, Math. Slovaca, 63 (2013) 817-828. [WoS] Zbl1340.34349
  10. [10] C. Wang, R.P. Agarwal, Relatively dense sets, corrected uniformly almost periodic functions on time scales, and generalizations, Adv. Differ. Equ., 312 (2015) 1-9. [Crossref] 
  11. [11] A. Wilansky, Topics in Functional Analysis, Springer, Lecture Notes in Mathematics, Volume 45 (1967).  Zbl0156.36103
  12. [12] Y. Li, B. Li, Almost periodic time scales and almost periodic functions on time scales, J. Appl. Math., (2015) 1-8 (Article ID 730672).  
  13. [13] B. Sendov, Hausdorff Approximations, Kluwer Academic Publishers, Netherlands, (1990).  

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