• 대한수학회논문집
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• 제22권4호
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• pp.535-545
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• 2007

In this paper, we introduce the Pettis integral of fuzzy mappings in Banach spaces using the Pettis integral of closed set-valued mappings. We investigate the relations between the Pettis integral, weak integral and integral of fuzzy mappings in Banach spaces and obtain some properties of the Pettis integral of fuzzy mappings in Banach spaces.

• 충청수학회지
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• 제21권4호
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• pp.427-435
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• 2008

In this paper, we give some extensions of Dunford integral and Pettis integral, C-Dunford integral and C-Pettis integral. We also discuss the relation among the C-Dunford integral, C-Pettis integral and C-integral.

• 충청수학회지
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• 제19권3호
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• pp.231-236
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• 2006

In this paper, we study the Henstock-Pettis integral of Banach space-valued functions mapping an interval [0, 1] in R into a Banach space X. In particular, we show that a Henstock integrable function on [0, 1] is Henstock-Pettis integrable on [0, 1] and a Pettis integrable function is Henstock-Pettis integrable on [0, 1].

• 충청수학회지
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• 제21권1호
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• pp.21-28
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• 2008

In this paper, we give the Riemann-type extensions of Dunford integral and Pettis integral, C-Dunford integral and C-Pettis integral. We prove that a function f is C-Dunford integrable if and only if $x^*f$ is C-integrable for each $x^*{\in}X^*$ and prove the controlled convergence theorem for the C-Pettis integral.

• Korean Journal of Mathematics
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• 제18권3호
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• pp.229-241
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• 2010

In this paper, we introduce the Denjoy-Pettis integral of fuzzy mappings in Banach spaces and obtain some properties of the Denjoy-Pettis integral of fuzzy mappings and the convergence theorems for Denjoy-Pettis integrable fuzzy mappings.

• 대한수학회논문집
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• 제24권2호
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• pp.227-237
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• 2009

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.

• Korean Journal of Mathematics
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• 제22권2호
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• pp.383-393
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• 2014

In this paper, we introduce the concept of Choquet-Pettis integral of Banach-valued functions using the Choquet integral of real-valued functions and investigate convergence theorems for the Choquet-Pettis integral.

• 충청수학회지
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• 제23권2호
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• pp.279-291
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• 2010

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.

• Korean Journal of Mathematics
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• 제20권4호
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• pp.381-393
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• 2012

In this paper, we introduce the Choquet-Pettis integral of set-valued mappings and investigate some properties and convergence theorems for the set-valued Choquet-Pettis integrals.

• Korean Journal of Mathematics
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• 제10권2호
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• pp.123-130
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• 2002

In this paper we introduce the concepts of Denjoy-Stieltjes-Dunford, Denjoy-Stieltjes-Pettis and Denjoy-Stieltjes-Bochner integrals of Banach-valued functions and then prove some properties of them.