An illustrative example for the Perron condition
Jacenty Kloch (1977)
Annales Polonici Mathematici
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Jacenty Kloch (1977)
Annales Polonici Mathematici
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Marian Jabłoński (1988)
Annales Polonici Mathematici
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M. Jabłoński, J. Malczak (1984)
Colloquium Mathematicae
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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.
Štefan Schwabik (1990)
Časopis pro pěstování matematiky
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Krishna B. Athreya, Peter Ney (1982)
Mathematische Zeitschrift
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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.
Ludwig F. Elsner, Christopher R. Johnson, M. Neumann (1982)
Czechoslovak Mathematical Journal
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