• Communications of the Korean Mathematical Society
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• v.22 no.4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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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].

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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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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• v.18 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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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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• v.22 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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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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• v.20 no.4
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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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• v.10 no.2
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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.