Abstract
We examine a way of using the parametric continuation method to compute mappings of the unit ball in $$n$$ -dimensional real space. The proposed approach yielded sufficient and necessary conditions for the global injectivity of mappings were obtained. It is established that these conditions actually coincide with the known features of the $$n$$ -dimensional complex space. The concretization of the method made here are the generalizations of some classes of functions analytic in the unit circle. In addition, the analogue of the Kaplan class was derived for mappings in $$n$$ -dimensional real space.
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