• 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.

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.315-327
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• 2008

In this paper we introduce the concepts of $Denjoy_*$-Stieltjes-Dunford, $Denjoy_*$-Stieltjes-Pettis, $Denjoy_*$-Stieltjes-Bochner and $Denjoy_*$-McShane-Stieltjes integrals of Banach-valued functions using the $Denjoy_*$-Stieltjes integral of real-valued functions and investigate their properties.

• Korean Journal of Mathematics
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• v.11 no.2
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• pp.137-146
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• 2003

In this paper we introduce the concepts of the weak $Denjoy_*$ integral of real-valued functions and the weak $Denjoy_*$-Dunford, weak $Denjoy_*$-Pettis, weak $Denjoy_*$-Bochner, weak $Denjoy_*$-McShane integrals of Banach-valued functions and then investigate some of their properties.

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.277-287
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• 1996

The theory of integration of functions with values in a Banach space has long been a fruitful area of study. In the eight years from 1933 to 1940, seminal papers in this area were written by Bochner, Gelfand, Pettis, Birhoff and Phillips. Out of this flourish of activity, two integrals have proved to be of lasting: the Bochner integral of strongly measurable function. Through the forty years since 1940, the Bochner integral has a thriving prosperous history. But unfortunately nearly forty years had passed until 1976 without a significant improvement after B. J. Pettis's original paper in 1938 [cf. 11].

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.879-884
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• 2010

In this paper, we introduce the AP-Henstock Dunford, AP-Henstock Pettis and AP-Henstock Bochner integral Banach-valued functions and investigate some properties of the these integrals.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.307-316
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• 1998

In this paper Denjoy*-Dunford, Denjoy*-Pettis, Denjoy*-McShane and Denjoy*-Bochner integrals of functions which map an interval [a,b] into a Banach space X are defined. And we give the relations among the integrals.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.285-295
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• 2013

In this note we present sufficient conditions for the existence of Radon-Nikodym derivatives (RND) of operator valued measures with respect to scalar measures. The RND is characterized by the Bochner integral in the strong operator topology of a strongly measurable operator valued function with respect to a nonnegative finite measure. Using this result we also obtain a characterization of compact sets in the space of operator valued measures. An extension of this result is also given using the theory of Pettis integral. These results have interesting applications in the study of evolution equations on Banach spaces driven by operator valued measures as structural controls.