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On the Birkhoff integral of fuzzy mappings in Banach spaces

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In this paper, we introduce the Birkhoff integral of fuzzy mappings in Banach spaces in terms of the Birkhoff integral of set-valued mappings and investigate some properties of the Birkhoff integrals of set-valued mappings and fuzzy mappings in Banach spaces.

Abstract

In this paper, we introduce the Birkhoff integral of fuzzy mappings in Banach spaces in terms of the Birkhoff integral of set-valued mappings and investigate some properties of the Birkhoff integrals of set-valued mappings and fuzzy mappings in Banach spaces.

참고문헌 (11)

  1. M. Balcerzak, "Convergence theorems for the Birkhoff integral", Czech. Math. J, 58, pp.1207~1219 (2008)
  2. G. Birkhoff, "Integration of functions with values in a Banach space", Trans. Amer. Math. Soc, 38, pp.357~378 (1935)
  3. B. Cascales, "Birkhoff integral for multi-valued functions", J. Math. Anal. Appl, 297, pp.540~560 (2004)
  4. B. Cascales, "The Birkhoff integral and the property of Bourgain", Math. Ann, 331, pp.259~279 (2005)
  5. C. Castaing, "Convex Analysis and Measurable Multifunctions", Lecture Notes in Math., 580 (1977), Springer-Verlag Berlin
  6. K. El Amri, "On the Pettis integral of closed valued multifunctions", Set-Valued Anal, 8, pp.329~360 (2000)
  7. V. Marraffa, "A charactirization of absolutely summing operators by means of McShane integrable functions", J. Math. Anal. Appl, 293, pp.71~78 (2004)
  8. B. J. Pettis, "On integration in vector spaces", Trans. Amer. Math. Soc, 44, pp.277~304 (1938)
  9. J. Rodriguez, "On the existence of Pettis integrable functions which are not Birkhoff integrable", Proc. Amer. Math. Soc, 133, pp.1157~1163 (2005)
  10. X. Xue, "Random fuzzy number integrals in Banach spaces", Fuzzy Sets and Systems, 66, pp.97~111 (1994)
  11. X. Xue, "On the convergence and representation of random fuzzy number integrals", Fuzzy Sets and Systems, 103, pp.115~125 (1999)

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