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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]

In this paper we formulate a version of the Kondurar theorem and a generalization of the Itô formula for functions taking values in Riesz spaces with respect to a convergence, satisfying suitable axioms. When the involved space is the space of measurable functions, both convergence almost everywhere and convergence in probability are included. Finally we present some comments and possible applications of the Itô formula. [ABSTRACT FROM AUTHOR]