On some properties of p-holomorphic and p-analytic function

In this article the relationship between the conditions of p-differentiability, p-holomorphycity, and the existence of the derivative of a function of a p-complex variable is considered. The general form of a p-holomorphic function is found. The sufficient conditions for p-analyticity and local invertibility are obtained. The open mapping theorem and the principle of maximum of the norm for a p-holomorphic function and the uniqueness theorem are proved.

On a Criterion of Local Invertibility and Conformality for Slice Regular Quaternionic Functions

A new criterion for local invertibility of slice regular quaternionic functions is obtained. This paper is motivated by the need to find a geometrical interpretation for analytic conditions on the real Jacobian associated with a slice regular function f. The criterion involves spherical and Cullen derivatives of f and gives rise to several geometric implications, including an application to related conformality properties.