Abstract
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.
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