Sharp Bounds for the Second Hankel Determinant of Logarithmic Coefficients for Strongly Starlike and Strongly Convex Functions

Abstract

The logarithmic coefficients are very essential in the problems of univalent functions theory. The importance of the logarithmic coefficients is due to the fact that the bounds on logarithmic coefficients of f can transfer to the Taylor coefficients of univalent functions themselves or to their powers, via the Lebedev–Milin inequalities; therefore, it is interesting to investigate the Hankel determinant whose entries are logarithmic coefficients. The main purpose of this paper is to obtain the sharp bounds for the second Hankel determinant of logarithmic coefficients of strongly starlike functions and strongly convex functions.

Keywords

• logarithmic coefficient
• Hankel determinant
• strongly starlike
• strongly convex