Univalence of a complex linear combination of two extremal parallel slit mappings

Masakazu Shiba

Any convex combination of the so-called extremal horizontal and vertical slit mappings of a plane domain is known to be univalent. In his study on the conformal welding of annuli F. Maitani needed to know when a complex linear combination is univalent and he gave a partial answer to this problem. In the present article we give a complete answer to his and to generalized problems.

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Analysis is devoted to the field of mathematical analysis, in particular classical analysis and its applications. Its aim is to publish the best research articles within the scope of the journal, as well as to boost the cooperation between scholars.