Expression of the Lebesgue Δ-integral on time scales as a usual Lebesgue integral; application to the calculus of Δ-antiderivatives

Authors:
Alberto Cabada;Dolores R. Vivero
Affiliations:
Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Galicia, Spain;Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Galicia, Spain
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2006

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Abstract

This paper is devoted to the study of the Lebesgue @D-integral on time scales. We give a formula in which such an integral is obtained as a sum of adequate real Lebesgue integrals. By using the relationship between these kinds of integrals and the Riemann ones, we rewrite the given expression to obtain the @D-antiderivatives of functions defined on time scales. The results obtained are illustrated with some examples.