Some extremal problems for Pairs of functions with no common values

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Abstract

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 + β01z+..., 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.

Original languageEnglish
Pages (from-to)3115-3123
Number of pages9
JournalJournal of Soviet Mathematics
Volume52
Issue number3
DOIs
StatePublished - Nov 1990

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