Coefficient estimates for $m$-fold symmetric bi-subordinate functions

Authors : Ebrahim A. Adegani, Samaneh G. Hamidi, Jay M. Jahangiri, Ahmad Zireh

Pages : 365-371

Doi:10.15672/hujms.545237

View : 19 | Download : 17

Publication Date : 2019-04-01

Article Type : Research

Abstract :A function is said to be bi-univalent in the open unit disk $\mathbb{U}$ if both the function and its inverse map are univalent in $\mathbb{U}$. By the same token, a function is said to be bi-subordinate in $\mathbb{U}$ if both the function and its inverse map are subordinate to a given function in $\mathbb{U}$. In this paper, we consider the m-fold symmtric transform of such functions and use their Faber polynomial expansions to find upper bounds for their n-th ($n\geq 3$) coefficients subject to a given gap series condition. We also determine bounds for the first two coefficients of such functions with no restrictions imposed.
Keywords : Faber polynomials, $m$-fold symmetric, bi-univalent functions