Faber Polynomial Coefficient Estimates for Meromorphic Bi-Starlike Functions

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.

Coefficients of Meromorphic Bi-Bazilevic Functions

“…The unexpected and unusual behavior of the coefficients of meromorphic functions and their inverses ℎ = −1 prove the investigation of the coefficient bounds for bi-univalent functions to be very challenging. In this paper we extend the results of Kapoor and Mishra [9] and Hamidi et al [10,11] to a larger class of meromorphic bi-univalent functions, namely, ( ; ). We conclude our paper with an examination of the unexpected behavior of the early coefficients of meromorphic bi-Bazilevic functions which is the best estimate yet appeared in the literature.…”

“…This restriction imposed on is a very tight restriction since the class ( ; 0) shrinks for large values of . More recently, Hamidi et al [10] (also see [11]) improved the coefficient estimate given by Kapoor and Mishra in [9].…”

Coefficient Estimates for Certain Classes of Bi-Univalent Functions

“…A function ∈ A is said to be bi-univalent in D if both ∈ S and = −1 ∈ S. Finding bounds for the coefficients of classes of bi-univalent functions dates back to 1967 (see Lewin [3]). But the interest on the bounds for the coefficients of classes of bi-univalent functions picked up by the publications of Brannan and Taha [4], Srivastava et al [5], Frasin and Aouf [6], Ali et al [7], and Hamidi et al [8]. The bi-univalency condition imposed on the functions ∈ A makes the behavior of their coefficients unpredictable.…”

Coeficient estimates for a subclass of meromorphic bi-univalent functions defined by subordination

“…But the interest on coefficient estimates of the meromorphic univalent functions keep on by many researchers, see for example, [18,19,25,26]. Several authors by using Faber polynomial expansions obtained coefficient estimates |a n | for classes meromorphic bi-univalent functions and bi-univalent functions, see for example [10,12,13,14,15,16,17,28,27]. First we recall some definitions and lemmas that used in this work.…”