The $M_\alpha $ and $C$-integrals

Title:

The $M_\alpha $ and $C$-integrals

Creator:

Park, Jae Myung, Ryu, Hyung Won, Lee, Hoe Kyoung, and Lee, Deuk Ho

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:05e6b09c-0195-42b9-afa7-1eaefccbd73f
uuid:05e6b09c-0195-42b9-afa7-1eaefccbd73f

Subject:

$M_\alpha $-integral and $ACG_\alpha $ function

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper, we define the $M_\alpha $-integral of real-valued functions defined on an interval $[a,b]$ and investigate important properties of the $M_{\alpha }$-integral. In particular, we show that a function $f\colon [a,b]\rightarrow R$ is $M_{\alpha }$-integrable on $[a,b]$ if and only if there exists an $ACG_{\alpha }$ function $F$ such that $F'=f$ almost everywhere on $[a,b]$. It can be seen easily that every McShane integrable function on $[a,b]$ is $M_{\alpha }$-integrable and every $M_{\alpha }$-integrable function on $[a,b]$ is Henstock integrable. In addition, we show that the $M_{\alpha }$-integral is equivalent to the $C$-integral.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

869-878

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:4

Harvested from:

CDK

Metadata only:

false