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

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 insert ignore into journalissuearticles values($n\geq 3$); coefficients subject to a given gap series condition. We also determine bounds for the first two coefficients of such functions with no restrictions imposed.