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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


A new characterization of Cesàro-Perron integrals using Peano derivates

Author: J. A. Bergin
Journal: Trans. Amer. Math. Soc. 228 (1977), 287-305
MSC: Primary 26A39
MathSciNet review: 0435312
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Abstract: The $ {Z_n}$-integrals are defined according to the method of Perron using Peano derivates. The properties of the integrals are given including the essential integration by parts theorem. The integrals are then shown to be equivalent to the Cesàro-Perron integrals of Burkill.

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PII: S 0002-9947(1977)0435312-0
Keywords: Cesàro-Perron integrals, Perron integral, Peano derivatives, integration by parts, generalized derivatives
Article copyright: © Copyright 1977 American Mathematical Society