• Korean Journal of Mathematics
• /
• v.17 no.3
• /
• pp.257-270
• /
• 2009

In this paper we introduce the Henstock integral of fuzzy mappings in Banach spaces as a generalization of the Henstock integral of set-valued mappings and investigate some properties of it.

• The Pure and Applied Mathematics
• /
• v.8 no.2
• /
• pp.87-99
• /
• 2001

In this paper, we define the Mcshane-Stieltjes integral for Banach-valued functions, and will investigate some of its properties and comparison with the Pettis integral.

• Journal of the Chungcheong Mathematical Society
• /
• v.5 no.1
• /
• pp.159-165
• /
• 1992

In 1986, R. Huff [3] showed that a Dunford integrable function is Pettis integrable if and only if T : $X^*{\rightarrow}L_1(\mu)$ is weakly compact operator and {$T(K(F,\varepsilon))|F{\subset}X$, F : finite and ${\varepsilon}$ > 0} = {0}. In this paper, we introduce the notion of Bourgain property of real valued functions formulated by J. Bourgain [2]. We show that the class of pettis integrable functions is linear space and if lis bounded function with Bourgain property, then T : $X^{**}{\rightarrow}L_1(\mu)$ by $T(x^{**})=x^{**}f$ is $weak^*$ - to - weak linear operator. Also, if operator T : $L_1(\mu){\rightarrow}X^*$ with Bourgain property, then we show that f is Pettis representable.

• Bulletin of the Korean Mathematical Society
• /
• v.21 no.1
• /
• pp.45-45
• /
• 1984

• Communications of the Korean Mathematical Society
• /
• v.13 no.2
• /
• pp.307-316
• /
• 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
• /
• v.28 no.2
• /
• pp.285-295
• /
• 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.

• The Pure and Applied Mathematics
• /
• v.7 no.1
• /
• pp.41-47
• /
• 2000

Johnson and Skoug [Pacific J. Math. 83(1979), 157-176] introduced the concept of scale-invariant measurability in Wiener space. And the applied their results in the theory of the Feynman integral. A converse measurability theorem for Wiener space due to the $K{\ddot{o}}ehler$ and Yeh-Wiener space due to Skoug[Proc. Amer. Math. Soc 57(1976), 304-310] is one of the key concept to their discussion. In this paper, we will extend the results on converse measurability in Wiener space which Chang and Ryu[Proc. Amer. Math, Soc. 104(1998), 835-839] obtained to abstract Wiener space.