On the Ninth Coefficient of the Inverse of a Convex Function

Toshiyuki Sugawa
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Toshiyuki Sugawa: Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579, Japan

Mathematics, 2021, vol. 9, issue 7, 1-5

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 .

Keywords: convex functions; inverse function; coefficient estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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