Displaying similar documents to “On ω-approximately continuous Denjoy-Steiltjes integral”

The s-Perron, sap-Perron and ap-McShane integrals

Joo Bong Kim, Deok Ho Lee, Woo Youl Lee, Chun-Gil Park, Jae Myung Park (2004)

Czechoslovak Mathematical Journal

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In this paper, we study the s-Perron, sap-Perron and ap-McShane integrals. In particular, we show that the s-Perron integral is equivalent to the McShane integral and that the sap-Perron integral is equivalent to the ap-McShane integral.

Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion

Tuo-Yeong Lee (2005)

Mathematica Bohemica

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It is shown that a Banach-valued Henstock-Kurzweil integrable function on an m -dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function f [ 0 , 1 ] 2 ⟶ ℝ and a continuous function F [ 0 , 1 ] 2 ⟶ ℝ such that ( ) ∫ 0 x ( ) ∫ 0 y f ( u , v ) d v d u = ( ) ∫ 0 y ( ) ∫ 0 x f ( u , v ) d u d v = F ( x , y ) for all ( x , y ) ∈ [ 0 , 1 ] 2 .

The ap-Denjoy and ap-Henstock integrals

Jae Myung Park, Jae Jung Oh, Chun-Gil Park, Deuk Ho Lee (2007)

Czechoslovak Mathematical Journal

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In this paper we define the ap-Denjoy integral and show that the ap-Denjoy integral is equivalent to the ap-Henstock integral and the integrals are equal.