• 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.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.