Some Sharp Results on Coefficient Estimate Problems for Four-Leaf-Type Bounded Turning Functions

Abstract

In this study, we focused on a subclass of bounded turning functions that are linked with a four-leaf-type domain. The primary goal of this study is to explore the limits of the first four initial coefficients, the Fekete-Szegö type inequality, the Zalcman inequality, the Kruskal inequality, and the estimation of the second-order Hankel determinant for functions in this class. All of the obtained findings have been sharp.

Subclasses of Analytic Functions Subordinated to the Four-Leaf Function

“…Remark 3. The results presented in this paper specifically for the case when r = 1 and s = 0 were previously obtained by Sunthrayuth et al [27].…”

“…Gandhi in [26] introduced a set of bounded turning functions connected to a threeleaf function. In 2022, in the articles [27,28] the authors introduced and studied different subclasses of analytic functions defined by subordination to the four-leaf function (see Figure 1, made with MAPLE™ 2023 computer software) that is given by…”

“…(ii) Putting s = 0 and r = 1 in (4), we obtain the class A 1,0 4 , which was introduced and studied by Sunthrayuth et al [27], which is…”

Some Results on Coefficient Estimate Problems for Four-Leaf-Type Bounded Turning Functions

“…In 2022, Sunthrayuth et al [12] introduced a subclass of bounded turning functions associated with a four-leaf function defined by…”