Faber Polynomial Coefficient Estimates for Meromorphic Bi-Starlike Functions

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We consider meromorphic starlike univalent functions that are also bi-starlike and find Faber polynomial coefficient estimates for these types of functions. A function is said to be bi-starlike if both the function and its inverse are starlike univalent. Consider the function í µí±” (í µí± §) = í µí± § + í µí± 0 + ∞ ∑ í µí±› = 1 í µí± í µí±› 1 í µí± § í µí±› , (1) where the coefficients are in the subman-ifold í µí±€ on í µí° ¶ í µí± such that í µí±”(í µí± §) is univalent in Δ := {í µí± § : 1 < |í µí± §| < ∞}. Therefore í µí± §í µí±” í® í° (í µí± §) í µí±” (í µí± §) = 1 + ∞ ∑ í µí±› = 0 í µí°¹ í µí±›+1 (í µí± 0 , í µí± 1 , í µí± 2 ,. .. , í µí± í µí±›) 1 í µí± § í µí±›+1 , (2) where í µí°¹ í µí±›+1 (í µí± 0 , í µí± 1 , í µí± 2 ,. .. , í µí± í µí±›) is a Faber polynomial of degree í µí±› + 1. (Also see [1, 2].) We note that í µí°¹ 1 = −í µí± 0 ,