Integral and Differential Calculus in Riesz spaces and applications.

In this paper we outline a new theory about integral and differential calculus for Riesz space-valued mappings defined on suitable Riesz spaces. In our abstract context, we prove some theorems similar to the classical ones, like for example the Fundamental Formula of Calculus and the theorem about exchanging order between limits and derivatives. As applications, we give some results about power series, a fixed point theorem, and some models of differential functional equations. [ABSTRACT FROM AUTHOR]