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Aumann Integral on Time Scales

DOI: 10.4236/oalib.1104254, PP. 1-6

Subject Areas: Mathematical Analysis

Keywords: Aumann Integral, Time Scales, Lebesgue △-Integral on Time Scales

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Abstract

In this paper, we consider by the first time the Aumann integral on time scales. Hence, we introduce the Aumann -integral on time scales. We also have established properties for the Aumann -integral on time scales. In particular, we obtain a formula that relates the Aumann -integral on time scales and the Aumann integral.

Cite this paper

Santos, I. L. D. D. (2018). Aumann Integral on Time Scales. Open Access Library Journal, 5, e4254. doi: http://dx.doi.org/10.4236/oalib.1104254.

References

[1]  Liu, D. and Zhao, D. (2012) On the McShane Integral on Time Scales. Chinese Quarterly Journal of Mathematics, 27, 556-561.
[2]  Mozyrska, D., Pawluszewicz, E. and Torres, D.F.M. (2010) The Riemann-Stieltjes Integral on Time Scales. The Aus-tralian Journal of Mathematical Analysis and Applications, 7, 1-14.
[3]  Peterson, A. and Thompson, B. (2006) Henstock-Kurzweil Delta and Nabla Integrals. Journal of Mathematical Analysis and Applications, 323, 162-178.
https://doi.org/10.1016/j.jmaa.2005.10.025
[4]  Guseinov, G.S. (2003) Integration on Time Scales. Journal of Mathematical Analysis and Applications, 285, 107-127.
https://doi.org/10.1016/S0022-247X(03)00361-5
[5]  Aumann, R.J. (1965) Integrals of Set-Valued Functions. Journal of Mathematical Analysis and Applications, 12, 1-12.
https://doi.org/10.1016/0022-247X(65)90049-1
[6]  Cabada, A. and Vivero, D.R. (2006) Expression of the Lebesgue △-Integral on Time Scales as a Usual Lebesgue Integral: Application to the Calculus of △-Antiderivatives. Mathematical and Computer Modelling, 43, 194-207.
https://doi.org/10.1016/j.mcm.2005.09.028
[7]  Santos, I.L.D. and Silva, G.N. (2013) Absolute Continuity and Existence of Solutions to Dynamic Inclusions in Time Scales. Mathematische Annalen, 356, 373-399.
https://doi.org/10.1007/s00208-012-0851-8
[8]  Castaing, C. and Valadier, M. (1977) Convex Analysis and Measurable Mul-tifunctions. Springer Lecture Notes in Mathematics, Vol. 580.
https://doi.org/10.1007/BFb0087685

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