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Convergence theorems for set-valued Denjoy-Pettis integrable mappings

Chun-Kee Park
대한수학회 (The Korean Mathematical Society)|2009.04|대한수학회논문집 (Communications of the KMS)|제24권 제2호|pp. 227-237

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참고문헌

키워드

set-valued mappingDenjoy integralDenjoy-Pettis integral
주제분류수학

초록

In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued Denjoy-Pettis integrable mappings.

Abstract

In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued Denjoy-Pettis integrable mappings.

참고문헌 (13)

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  2. B. Cascales, "Birkhoff integral for multi-valued functions", J. Math. Anal. Appl., 297, pp.540~560 (2004)
  3. G. Debreu, "Integration of Correspondences" (1967), Univ. California Press
  4. L. Di Piazza, "A decomposition theorem for compact-valued Henstock integral", Monatsh. Math., 148, pp.119~126 (2006)
  5. L. Di Piazza, "Set-valued Kurzweil-Henstock-Pettis integral", Set-Valued Analysis, 13, pp.167~179 (2005)
  6. K. El Amri, "On the Pettis integral of closed valued multifunctions", Set-Valued Analysis, 8, pp.329~360 (2000)
  7. J. L. Gamez, "On Denjoy-Dunford and Denjoy-Pettis integrals", Studia Math., 130, pp.115~133 (1998)
  8. R. A. Gordon, "The Denjoy extension of the Bochner, Pettis and Dunford integrals", Studia Math., 92, pp.73~91 (1989)
  9. R. A. Gordon, "The Integrals of Lebesgue, Denjoy, Perron and Henstock", Grad. Stud. Math., 4 (1994), Amer. Math. Soc.
  10. N. Papageoriou, "On the theory of Banach space valued multifunctions", J. Multivariate Anal., 17, pp.185~206 (1985)
  11. S. Saks, "Theory of the Integral" (1964), Dover
  12. J. Wu, "The w-derivatives of fuzzy mappings in Banach spaces", Fuzzy Setsand Systems, 119, pp.375~381 (2001)
  13. W. Zhang, "Set-Valued Stochastic Process" (1996), Academic Press

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