Some extremal problems for Pairs of functions with no common values

By the method of the moduli of families of curves one solves some extremal problems in the family of pairs {f₁, f₂} of functions f₁(z)=αz + ..., f₂(z)=βz^-1 + β⁰ +β¹z+..., with real coefficients, univalent, regular, resp. meromorphic in the circle Δ={∥z∥<1} and mapping onto nonoverlapping domains. As a special case the solution of a problem, posed by V. M. Miklyukov in Sib. Mat. Zh., Vol. 18, 1977, No. 5, pp. 1111–1124, is obtained. Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 160, pp. 159–169, 1987.