Coefficient functionals for Sakaguchi-type-Starlike functions subordinated to the three-leaf function

Abstract

A challenging part of studying geometric function theory is figuring out the sharp boundaries for coefficient-related problems that crop up in the Taylor-Maclaurin series of univalent functions. The objective of this article is to define the families of Sakaguchi-type starlike functions with respect to symmetric points based on qq-operator and to investigate the precise boundaries for a range of issues, including the first three initial coefficient estimates, Fekete-Szegö type and the Zalcman inequalities by subordinating to the function of the three leaves. Additionally, we discussed initial coefficients and Fekete-Szegö type inequalities for functions of the form ℱ−1{{\mathcal{ {\mathcal F} }}}^{-1} and zℱ(z)\frac{z}{{\mathcal{ {\mathcal F} }}\left(z)} and 12logℱ(z)z\frac{1}{2}\log \left(\phantom{\rule[-0.75em]{}{0ex}},\frac{{\mathcal{ {\mathcal F} }}(z)}{z}\right) linked with the function of the three leaves.

Keywords

• analytic functions
• subordination
• three-leaf function
• convolution
• coefficient inequalities
• fekete-szegő functional
• krushkal inequality
• 30c45
• 30c50