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In the paper [1] considered a new class of quaternionic mappings, so-called$G$-monogenic mappings. In this paper we prove analogues of classical integraltheorems of the holomorphic function theory: the Cauchy integral theorems forsurface and curvilinear integrals, and the Cauchy integral formula for$G$-monogenic mappings.

Integral theorems for the quaternionic G-monogenic mappings