On a maximal outer area problem for a class of meromorphic univalent fuctions

Stephen M. Zemyan

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

For 0 < p < 1, let Sp denote the class of functions f (z) which are meromorphic and univalent in the unit disk U, with the normalisations f (0) = 0, f”(0) = 1 and f (p) = ∞, and let Sp (a) denote subclass of Sp consisting of those functions in Sp whose residue at the pole in equal to a. In this paper, we determine, for values of the residue a in a certain disk Δp, the greatest possible outer area over all functions in the class Sp (a). We also determine additional information concerning extremal function if the reside a dose not lie in Δp.

Original languageEnglish (US)
Pages (from-to)433-445
Number of pages13
JournalBulletin of the Australian Mathematical Society
Volume34
Issue number3
DOIs
StatePublished - Dec 1986

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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