A Perron-type integral of order k for Riesz space-valued functions is defined in terms of the Peano derivatives. Some fundamental properties of this integral, including an integration by parts formula, are presented. We use the tools of Differential and Integral Calculus in Riesz spaces, the divided differences, the k-convexity and some regularity properties of the major and minor functions involved. We use also the Maeda-Ogasawara-Vulikh Riesz representation theorem.
The Perron Integral of order k in Riesz Spaces
BOCCUTO, Antonio;
2010
Abstract
A Perron-type integral of order k for Riesz space-valued functions is defined in terms of the Peano derivatives. Some fundamental properties of this integral, including an integration by parts formula, are presented. We use the tools of Differential and Integral Calculus in Riesz spaces, the divided differences, the k-convexity and some regularity properties of the major and minor functions involved. We use also the Maeda-Ogasawara-Vulikh Riesz representation theorem.File in questo prodotto:
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