Interior estimates of first order for initial value problems in the octonion algebra

Abstract

In this paper we use a Cauchy-Type integral formula for analytic octonionic-valued functions, to give an interior estimate of first order, in the supremum norm, for such functions. These estimates are used to solve an initial value problem with a O-analytic function as initial data, via the Banach fixed point theorem.

Keywords

• interior estimates
• octonions
• o-analytic functions
• initial value problem