Year: 2026
Type: article
Abstract: We introduce the mixed-order classes C [ M ] r , s by combining mixed differentiability with the weight-matrix framework, in both the Beurling and Roumieu cases. At finite order we prove a chain rule under the Faà-di-Bruno property. The currying map is a linear injection. If r and s are finite, the class coincides with C r , s and the exponential law reduces to the mixed-order law without weights. Continuity of the inverse on the image holds when a lower weight bound is available at a single index.
Author: Hamza Alzaareer
Institution: Al-Zaytoonah University of Jordan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7221654074