On the range of one complex-valued functional

V. A. Pchelintsev, E. A. Pchelintsev

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We solve the problem of finding the range Ω of one functional on the class of pairs of normalized univalent functions. Using the method of internal variations, we obtain a system of functionaldifferential equations for the boundary functions solved in quadratures. We prove that the range of the functional is some disk centered at the origin of a radius depending on the parameters of the functional.

Original languageEnglish
Pages (from-to)922-928
Number of pages7
JournalSiberian Mathematical Journal
Volume56
Issue number5
DOIs
Publication statusPublished - 1 Sep 2015

Keywords

  • boundary function
  • functional
  • range
  • univalent function
  • variational method

ASJC Scopus subject areas

  • Mathematics(all)

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