Abstract
For a quasi-balanced domain, we study holomorphic mappings \({F : D \times D \to D}\) such that F(z, z) = z and F(z, w) = F(w, z) for any \({z, w \in D}\). We show that in many cases the existence of such a function is equivalent to the convexity of the domain D.
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Research partially supported by the National Science Center of Poland (NCN) Grant UMO-2011/03/B/ST1/04758.
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Edigarian, A. Balanced domains and convexity. Arch. Math. 101, 373–379 (2013). https://doi.org/10.1007/s00013-013-0567-3
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DOI: https://doi.org/10.1007/s00013-013-0567-3