Displaying similar documents to “An illustrative example for the Perron condition”

Some remarks on comparison functions

Antoni Augustynowicz (2009)

Annales Polonici Mathematici

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We answer some questions concerning Perron and Kamke comparison functions satisfying the Carathéodory condition. In particular, we show that a Perron function multiplied by a constant may not be a Perron function, and that not every comparison function is bounded by a comparison function with separated variables. Moreover, we investigate when a sum of Perron functions is a Perron function. We also present a criterion for comparison functions with separated variables.

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 and a continuous function F [ 0 , 1 ] 2 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 .