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

Year 2019, Volume: 48 Issue: 2, 365 - 371, 01.04.2019

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

https://doi.org/10.15672/hujms.545237

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

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