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- Title
On the Ninth Coefficient of the Inverse of a Convex Function.
- Authors
Sugawa, Toshiyuki; Bulboacă, Teodor
- Abstract
We consider the inverse function z = g (w) = w + b 2 w 2 + ⋯ of a normalized convex univalent function w = f (z) = z + a 2 z 2 + ⋯ on the unit disk in the complex plane. So far, it is known that | b n | ≤ 1 for n = 2 , 3 , ⋯ , 8. On the other hand, the inequality | b n | ≤ 1 is not valid for n = 10. It is conjectured that | b 9 | ≤ 1. The present paper offers the estimate | b 9 | < 1.617.
- Subjects
UNIVALENT functions; INVERSE functions; CONVEX functions
- Publication
Mathematics (2227-7390), 2021, Vol 9, Issue 7, p706
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math9070706