Best Bounds for Fekete-Szegö Functional for the kth Root Transform of Certain Subclasses of Sakaguchi Type functions

Abstract

In recent research, working on coefficient bounds is very popular and useful to deal with geometric properties of the underlying functions. In this work, two new subclasses of Sakaguchi type functions with respect to symmetric points through subordination are considered. Moreover, the initial coefficients and the sharp upper bounds for the functional $|\rho_{2k+1}-\mu \rho_{k+1}^{2}|$ corresponding to $k^{th}$ root transformation belong to the above classes are obtained and thoroughly investigated.