Construction of Sufficient Univalent Conditions in Domains Convex in a Sector of Directions

Аннотация

We study the domains which are convex in a sector of directions. Subclasses of domains whose boundaries are quasiconformal curves are determined and some sufficient univalent conditions are constructed for functions analytic in these domains. In addition, applications of the obtained results to the strong problem of univalence in inverse boundary value problems are discussed.