Table of Contents Author Guidelines Submit a Manuscript
International Journal of Stochastic Analysis
Volume 2015 (2015), Article ID 834194, 5 pages
http://dx.doi.org/10.1155/2015/834194
Research Article

On Continuous Selection Sets of Non-Lipschitzian Quantum Stochastic Evolution Inclusions

Department of Mathematics, Covenant University, KM 10 Idiroko Road, PMB 1023, Ota, Ogun State, Nigeria

Received 25 March 2015; Accepted 7 July 2015

Academic Editor: Alexander M. Krasnosel’skii

Copyright © 2015 Sheila Bishop. 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.

Linked References

  1. M. O. Ogundiran, “Continuous selections of solution sets of quantum stochastic evolution inclusion,” Journal of Nonlinear Functional Analysis, vol. 2014, article 4, 2014. View at Google Scholar
  2. E. O. Ayoola, “Continuous selections of solution sets of lipschitzian quantum stochastic differential inclusions,” International Journal of Theoretical Physics, vol. 43, no. 10, pp. 2041–2059, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. A. Cellina, “On the set of solutions to Lipschitzian differential inclusions,” Differential and Integral Equations, vol. 1, no. 4, pp. 495–500, 1988. View at Google Scholar · View at MathSciNet
  4. J.-P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin, Germany, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  5. A. F. Filippov, “Classical solutions of differential equations with multi-valued right-hand side,” SIAM Journal on Control and Optimization, vol. 5, pp. 609–621, 1967. View at Publisher · View at Google Scholar · View at MathSciNet
  6. M. Kisielewicz, Differential Inclusions and Optimal Control, vol. 44 of Mathematics and Its Applications (East European Series), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991.
  7. E. O. Ayoola, “Further results on the existence of continuous selections of solution sets of quantum stochastic differential inclusions,” Dynamic Systems and Applications, vol. 17, no. 3-4, pp. 609–624, 2008. View at Google Scholar · View at MathSciNet
  8. S. A. Bishop and T. A. Anake, “Extension of continuous selection sets to non-lipschitzian quantum stochastic differential inclusion,” Stochastic Analysis and Applications, vol. 31, no. 6, pp. 1114–1124, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. G. O. Ekhaguere, “Quantum stochastic differential inclusions of hypermaximal monotone type,” International Journal of Theoretical Physics, vol. 34, no. 3, pp. 323–353, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. E. O. Ayoola, “Construction of approximate attainability sets for Lipschitzian quantum stochastic differential inclusions,” Stochastic Analysis and Applications, vol. 19, no. 3, pp. 461–471, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. E. O. Ayoola, “Error estimates for discretized quantum stochastic differential inclusions,” Stochastic Analysis and Applications, vol. 21, no. 6, pp. 1215–1230, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. E. O. Ayoola, “Topological properties of solution sets of Lipschitzian quantum stochastic differential inclusions,” Acta Applicandae Mathematicae, vol. 100, no. 1, pp. 15–37, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. G. O. Ekhaguere, “Lipschitzian quantum stochastic differential inclusions,” International Journal of Theoretical Physics, vol. 31, no. 11, pp. 2003–2027, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. R. L. Hudson and K. R. Parthasarathy, “Quantum Ito's formula and stochastic evolutions,” Communications in Mathematical Physics, vol. 93, no. 3, pp. 301–323, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  15. G. O. S. Ekhaguere, “Quantum stochastic evolutions,” International Journal of Theoretical Physics, vol. 35, no. 9, pp. 1909–1946, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus