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.

A Fractional Differential Operator Based on Quantum Calculus and Bi-Close-to-Convex Functions

“…Recent studies, like [49], have shown that the classes could be studied further when the strong starlikeness of order α of the operator (λ, q)-fractional differintegral operator can be taken into consideration.…”

New Developments in Geometric Function Theory

“…Considering the importance of the logarithmic coefficients, in reference [8], Sevtap Sümer Eker, Bilal Şeker, Bilal Çekiç, and Mugur Acu obtain the sharp bounds for the second Hankel determinant concerning the logarithmic coefficients of strongly starlike functions and strongly convex functions. The results presented here could inspire further studies that focus on other subclasses of univalent functions and obtain the boundaries for higher-order Hankel determinants.…”

Problems Concerning Coefficients of Symmetric Starlike Functions Connected with the Sigmoid Function

“…For further investigations of the Hankel determinant on logarithmic coefficients, see [57][58][59][60]. In this section, we compute the sharp estimates of logarithmic coefficients up to µ 3 and Fekete-Szegö, Zalcman, and Krushkal inequalities along with the Hankel determinant H 2,1 G g /2 for the class SS * SG .…”