• Bulletin of the Korean Mathematical Society
• /
• v.42 no.3
• /
• pp.535-541
• /
• 2005

In this paper, we define the ap-Denjoy integral and investigate some properties of the ap-Denjoy integral.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.4
• /
• pp.543-550
• /
• 2007

In this paper, we define the ap-Denjoy integral and investigate some properties od the ap-Denjoy integral. In particular, we show that a function f : [a,b]${\rightarrow}\mathbb{R}$ is ap-Denjoy integrable on [a,b] if and only if there exists an $ACG_s$ function F on [a,b] such that $F^{\prime}_{ap}=f$ almost everywhere on [a,b].

• The Pure and Applied Mathematics
• /
• v.15 no.3
• /
• pp.343-351
• /
• 2008

In this paper, we define the Denjoy and ap-Denjoy integrals of Banach-valued functions, and we investigate some properties of these two integrals. In particular, we show that a Denjoy integrable function is ap-Denjoy integrable.

• Journal of the Chungcheong Mathematical Society
• /
• v.17 no.1
• /
• pp.103-110
• /
• 2004

In this paper, we define the ap-Denjoy integral and investigate some properties of the ap-Denjoy integral.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.1
• /
• pp.79-89
• /
• 2008

In this paper, we define the ap-Henstock integral and the ap-Denjoy integral of Banach-valued functions, and we investigate some properties of these two integrals. In particular, we show that the ap-Henstock integral is equivalent to the ap-Denjoy integral.