Fueter’s Theorem for One Class of Pseudoanalytic Functions

In this paper, we extend Fueter’s theorem in hypercomplex function theory to encompass a class of pseudoanalytic functions associated with the main Vekua equation. This class includes Duffin’s \(\mu \) $\mu$ -regular functions as special cases, which correspond to the Yukawa equation. As the parameter \(\mu \rightarrow 0\) $\mu \to 0$ , we recover the classical Fueter’s theorem.