Solving one extreme problem in a class of locally single-leaf functions

The central place in the theory of conformal maps is occupied by the solution of extreme problems on classes of single-leaf maps. In the known classes of normalized holomorphic functions S and C, the solution of the "coefficient problem" is associated with obtaining accurate estimates of the modules of the Taylor coefficients of class elements. Similar problems are posed for classes of locally single-leaf mappings. V.G.Sheretov introduced classes of locally conformal mappings generated using integral structural formulas from elements of classes S and C. The article solves the problem of an accurate estimation of the modulus of the Taylor coefficient in this class.