The quaternionic valued functions of a quaternionic variable, often referred to as slice regular functions, has been studied extensively due to the large number of generalized results of the theory of one complex variable. Recently, several global properties of these functions has been found such as a Borel–Pompieu formula and a Stokes’ Theorem from the study of a differential operator, see González-Cervantes and González-Campos (Complex Var Ellipt Equ 66(5):1–10, 2021, https://doi.org/10.1080/17476933.2020.1738410). The aim of this paper is to present a kind of quaternionic generalized slice regular functions that on slices coincide with pairs of complex generalized holomorphic functions associated to Vekua problems. The global properties of these functions are obtained from a perturbed global-type operator and among their local properties presented in this work are the versions of Splitting Lemma, Representation Theorem and a conformal property.

四元数变量的四元值函数，通常称为切片正则函数，由于一复变量理论的大量推广结果而得到了广泛的研究。最近，从微分算子的研究中发现了这些函数的几个全局属性，例如 Borel-Pompieu 公式和斯托克斯定理，参见 González-Cervantes 和 González-Campos (Complex Var Ellipt Equ 66(5):1 –2021 年 10 月，https://doi.org/10.1080/17476933.2020.1738410)。本文的目的是提出一种四元数广义切片正则函数，它在切片上与与 Vekua 问题相关的复数广义全纯函数对一致。