Logarithmic Coefficients of Some Close-to-Convex Functions

Abstract

Abstract. The logarithmic coefficients γ n of an analytic and univalent function f in the unit disk D = {z ∈ C : |z| < 1} with the normalization for functions in a subclass of close-to-convex functions (with argument 0) and claimed that the estimate is sharp by providing a form of a extremal function. In the present paper, we pointed out that such extremal functions do not exist and the estimate is not sharp by providing a much more improved bound for the whole class of close-to-convex functions (with argument 0). We also determine a sharp upper bound of |γ 3 | for close-to-convex functions (with argument 0) with respect to the Koebe function.

Coefficient Estimate on Second Hankel Determinant of the Logarithmic Coefficients for Close-To-Convex Function Subclass with Respect to the Koebe Function

“…The study of logarithmic coefficients has recently attracted the public's curiosity. [1], [2], [5], [8], [9], [11], [17], [18], [22] and [23], are just a few examples of logarithmic coefficient estimations that have been established.…”

The Order of Strongly Starlikeness of the Generalized α-Convex Functions

“…The strongly-starlike functions and related functions have been extensively studied by several authors (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]).…”