On Coefficient Problems for Functions Connected with the Sine Function

Abstract

In this paper, some coefficient problems for starlike analytic functions with respect to symmetric points are considered. Bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates for the following: coefficients, logarithmic coefficients, some cases of the generalized Zalcman coefficient functional, and some cases of the Hankel determinant.

Hankel Determinants for the Logarithmic Coefficients of a Subclass of Close-to-Star Functions

“…It is worth noting that knowing everything about B 0 , including estimates of coefcient functionals, is a good tool in studies of other classes of analytic functions. Using these results, one can easily obtain the fourth and ffth Hankel determinants as studied in the articles [20][21][22][23].…”

Certain Coefficient Estimate Problems for Three-Leaf-Type Starlike Functions

“…In 1966-1967, Pommerenke defined the Hankel determinant, but it was not evaluated till the year 2010. In 2010, Babalola [34] was the first researcher who worked on H 3,1 ( f ) and successfully obtained the upper bounds of |H 3,1 ( f )| related to the classes S * , K and R. Following this result, a few researchers extended this work for the various subcollections of univalent and holomorphic functions; see [35][36][37][38][39][40][41][42][43][44][45][46][47].…”