Geodesic
Theory of nonunivalent mappings of multiply connected domains
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 4, Tome 112 (1981), pp. 184-197

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In this paper one investigates new classes of regular functions in arbitrary domains, both with one and two distinguished boundary components. Special cases of these classes are the classes of mappings considered by Yu. E. Alenitsyn, I. P. Mityuk, and T. Kubo. 
@article{ZNSL_1981_112_a14,
     author = {V. A. Shlyk},
     title = {Theory of nonunivalent mappings of multiply connected domains},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {184--197},
     publisher = {mathdoc},
     volume = {112},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_112_a14/}
}
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V. A. Shlyk. Theory of nonunivalent mappings of multiply connected domains. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 4, Tome 112 (1981), pp. 184-197. http://geodesic.mathdoc.fr/item/ZNSL_1981_112_a14/