• Journal of the Chungcheong Mathematical Society
• /
• v.12 no.1
• /
• pp.179-186
• /
• 1999

In this paper, we define the Henstock-Stieltjes representable and nearly Henstock-Stieltjes representable operators for vector-valued function, which are the generalizations of Pettis representable operator and then study some properties of these operators.

• The Pure and Applied Mathematics
• /
• v.14 no.2 s.36
• /
• pp.71-84
• /
• 2007

In this paper, we define the C-Stieltjes integral of the functions mapping an interval [a,b] into a Banach space X with respect to g on [a,b], and the C-Stieltjes representable operators for the vector-valued functions which are the generalizations of the Henstock-Stieltjes representable operators. Some properties of the C-Stieltjes operators and the convergence theorems of the C-Stieltjes integral are given.