Abstract
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.
Highlights
We consider meromorphic starlike univalent functions that are bi-starlike and find Faber polynomial coefficient estimates for these types of functions
The Faber polynomials introduced by Faber [4] play an important role in various areas of mathematical sciences, especially in geometric function theory
Estimates on the coefficients of meromorphic univalent functions were widely investigated in the literature
Summary
We consider meromorphic starlike univalent functions that are 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. . .) are in the submanifold M on CN such that g(z) is univalent in Δ := {z : 1 < |z| < ∞}. Bn) is a Faber polynomial of degree n + 1. ( see [1, 2].) We note that. F1 = −b0, F2 = b02 − 2b1, F3 = −b03 + 3b1b0 − 3b2, F4 = b04 − 4b02b1 + 4b0b2 + 2b12 − 4b3, F5 = −b05 + 5b03b1 − 5b02b2 − 5b0b12 + 5b1b2 + 5b0b3 − 5b4, F6 = b06 + 3b22 + 6b03b2 − 12b0b1b2 − 6b04b1 − 2b13
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