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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.1 Antofagasta mar. 2019

http://dx.doi.org/10.4067/S0716-09172019000100097 

Articles

Asymptotic behavior of linear advanced dynamic equations on time scales

Malik Belaid1 

Abdelouaheb Ardjouni2 

Ahcene Djoudi3 

1University of Annaba, Department of Mathematics, Faculty of Sciences, Applied Mathematics Lab, P. O. Box 12, Annaba 23000, Algeria, e-mail: malikbelaid51@gmail.com

2University of Souk Ahras, Department of Mathematics and Informatics, P. O. Box 1553, Souk Ahras 41000, Algeria, e-mail: abd ardjouni@yahoo.fr

3University of Annaba, Faculty of Sciences, Applied Mathematics Lab, Department of Mathematics, P. O. Box 12, Annaba 23000, Algeria, e-mail: adjoudi@yahoo.com

Abstract

Let T be a time scale which is unbounded above and below and such that t0 T. Let id be such that are time scales. We use the contraction mapping theorem to obtain convergence to zero about the solution for the following linear advanced dynamic equation

where is the -derivative on T. A convergence theorem with a necessary and sufficient condition is proved. The results obtained here extend the work of Dung (11). In addition, the case of the equation with several terms is studied.

Keywords : Fixed points; advanced dynamic equations; Asymptotic

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgements.

The authors would like to thank the anonymous referee for his valuable comments.

References

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Received: January 2018; Accepted: October 2018

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