Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions

This is the authors' abstract. We don't add key points for this paper.

This article aims to determine the sharp bounds for the logarithmic coefficients of inverse functions in several classes of univalent functions. We obtain the sharp bounds of logarithmic coefficients Γ 1 , Γ 2 and Γ 3 of the inverse functions for the classes of starlike and convex functions with respect to symmetric points respectively. In addition, we establish sharp inequalities for the second Hankel determinant <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mfenced open="|" close="|"> <m:mrow> <m:msub> <m:mi>H</m:mi> <m:mrow> <m:mn>2</m:mn> <m:mo>,</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mfenced open="(" close=")"> <m:mrow> <m:msub> <m:mi>F</m:mi> <m:mrow> <m:mi>f</m:mi> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mrow> <m:mo>/</m:mo> </m:mrow> <m:mn>2</m:mn> </m:mrow> </m:mfenced> </m:mrow> </m:mfenced> <m:mo>≤</m:mo> <m:mn>3</m:mn> <m:mrow> <m:mo>/</m:mo> </m:mrow> <m:mn>44</m:mn> </m:math> |H2,1(Ff-1 / 2)| ≤ 3 / 44 and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mfenced open="|" close="|"> <m:mrow> <m:msub> <m:mi>H</m:mi> <m:mrow> <m:mn>2</m:mn> <m:mo>,</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mfenced open="(" close=")"> <m:mrow> <m:msub> <m:mi>F</m:mi> <m:mrow> <m:msup> <m:mi>f</m:mi> <m:mrow> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> </m:mrow> </m:msub> <m:mrow> <m:mo>/</m:mo> </m:mrow> <m:mn>2</m:mn> </m:mrow> </m:mfenced> </m:mrow> </m:mfenced> <m:mo>≤</m:mo> <m:mn>23</m:mn> <m:mrow> <m:mo>/</m:mo> </m:mrow> <m:mn>3264</m:mn> </m:math> |H2,1(F_f⁻¹ / 2)| ≤ 23 / 3264 of logarithmic coefficients of the inverse functions for starlike and convex functions associated with a lune region, where f − 1 is the inverse function of f .