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International Journal of Mathematics and Mathematical Sciences
Volume 2008, Article ID 465909, 13 pages
Research Article

On Some Inequalities of Uncertainty Principles Type in Quantum Calculus

1Faculté des Sciences de Tunis, Université de Tunis El Manar, 1060 Tunis, Tunisia
2Institut Préparatoire aux Études d'Ingénieur de Monastir, Université de Monastir, 5000 Monastir, Tunisia
3Institut de Biotechnologie, Université de Jendouba, 9000 Béja, Tunisia

Received 19 July 2007; Revised 31 January 2008; Accepted 14 April 2008

Academic Editor: Wolfgang Castell

Copyright © 2008 Ahmed Fitouhi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this paper is to generalize the 𝑞 -Heisenberg uncertainty principles studied by Bettaibi et al. (2007), to state local uncertainty principles for the 𝑞 -Fourier-cosine, the 𝑞 -Fourier-sine, and the 𝑞 -Bessel-Fourier transforms, then to provide an inequality of Heisenberg-Weyl-type for the 𝑞 -Bessel-Fourier transform.