Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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CONVERGENCE THEOREM FOR KURZWEIL-HENSTOCK-PETTIS INTEGRABLE FUZZY MAPPINGS

  • Park, Chun-Kee (Department of Mathematics Kangwon National University)
  • Received : 2010.03.02
  • Accepted : 2010.04.23
  • Published : 2010.06.30
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Abstract

In this paper, we introduce the Kurzweil-Henstock-Pettis integral of fuzzy mappings in Banach spaces in terms of the Kurzweil-Henstock-Pettis integral of set-valued mappings and obtain some properties of the Kurzweil-Henstock-Pettis integral of fuzzy mappings in Banach spaces and the convergence theorem for Kurzweil-Henstock-Pettis integrable fuzzy mappings.

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References

  1. R. J. Aumann Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965), 1-12. https://doi.org/10.1016/0022-247X(65)90049-1
  2. L. Di Piazza and K. Musial, A decomposition theorem for compact-valued Henstock integral, Monatsh. Math. 148 (2006), 119-126. https://doi.org/10.1007/s00605-005-0376-2
  3. L. Di Piazza and K. Musial, Set-valued Kurzweil-Henstock-Pettis integral, Set-Valued Analysis 13 (2005), 167-179. https://doi.org/10.1007/s11228-004-0934-0
  4. K. El Amri and C. Hess, On the Pettis integral of closed valued multifunctions, Set-Valued Analysis 8 (2000), 329-360. https://doi.org/10.1023/A:1026547222209
  5. D. H. Fremlin, The Henstock and McShane integrals of vector-valued functions, Illinois J. Math. 38 (1994), 471-479.
  6. R. A. Gordon, The integrals of Lebesgue, Denjoy, Perron and Henstock, Grad. Stud. Math. 4, Amer. Math. Soc. 1994.
  7. Guoju Ye, On Henstock-Kurzweil and McShane integrals of Banach space-valued functions, J. Math. Anal. Appl. 330 (2007), 753-765. https://doi.org/10.1016/j.jmaa.2006.08.020
  8. J. Wu and C. Wu, The w-derivatives of fuzzy mappings in Banach spaces, Fuzzy Sets and Systems 119 (2001) 375-381. https://doi.org/10.1016/S0165-0114(98)00468-0
  9. O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems 24 (1987), 301-317. https://doi.org/10.1016/0165-0114(87)90029-7
  10. N. Papageoriou, On the theory of Banach space valued multifunctions, J. Multivariate Anal. 17 (1985), 185-206. https://doi.org/10.1016/0047-259X(85)90078-8
  11. X. Xue, M. Ha and M. Ma, Random fuzzy number integrals in Banach spaces, Fuzzy Sets and Systems 66 (1994), 97-111. https://doi.org/10.1016/0165-0114(94)90303-4
  12. X. Xue, X. Wang and L. Wu, On the convergence and representation of random fuzzy number integrals, Fuzzy Sets and Systems, 103 (1999), 115-125. https://doi.org/10.1016/S0165-0114(97)00150-4