We solve the problem of finding the range E of some functional on the class of pairs of functions univalent in the system of the disk and the interior of the disk for the arbitrary parameters characterizing the functional. We prove that E is connected and bounded. Using the method of internal variations and the parametric method, we find the equation of the boundary of E. The obtained results extend Lebedev's study .
- elliptic integrals
- method of internal variations
- nonoverlapping domains
- parametric method
ASJC Scopus subject areas