Regulated Functions with values in the Banach Algebra of Quaternions

In this paper we deal with the notion of regulated functions with values in a Banach algebra A, we prove some results and present examples using quaternions. The physical meanning of this kind of functions is introduced and some particular results are presented. We consider then, the Dushnik integral for these functions and we construct a correspondent linear integral functional on the Banach algebra of all regulated functions G([a, b], A).