On the ninth coefficient of the inverse of a convex function

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Abstract

We consider the inverse function z = g(w) = w + b2w2 +…of a normalized convex univalent function w = f (z) = z + a2z2 +…on the unit disk in the complex plane. So far, it is known that {divides}bn{divides} ≥ 1 for n = 2, 3,…, 8. On the other hand, the inequality {divides}bn{divides} ≥ 1 is not valid for n = 10. It is conjectured that {divides}b9{divides} ≥ 1. The present paper offers the estimate {divides}b9{divides} < 1.617.

Original languageEnglish
Article number706
JournalMathematics
Volume9
Issue number7
DOIs
Publication statusPublished - 2021 Apr 1

Keywords

  • Coefficient estimates
  • Convex functions
  • Inverse function

ASJC Scopus subject areas

  • Mathematics(all)

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