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On Integrals of Vector-valued Functions on Time Scales

Commun. Math. Anal.
Volume 11, Number 1 (2011), 94 - 110

On Integrals of Vector-valued Functions on Time Scales

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Abstract

The main goal of the paper is to define new type of integrals for vector-valued functions on time scales. This allows to make possible the advantages of dynamic equations also for vector-valued functions i.e. for dynamic modeling in Banach spaces. To do it we define some appropriate integrals for vector-valued functions on time scales and we prove their properties. We emphasize on the particular ones, which are useful for solving dynamic equations in Banach spaces.