Faber polynomial coefficient estimates for analytic bi-close-to-convex functions

Faber polynomial coefficient estimates for certain classes of bi-univalent functions defined by using the Jackson (p,q)-derivative operator

“…In the literature, there are only a few works determining the general coefficient bounds |a n | for the analytic bi-univalent functions ( [7,16,18]). …”

Coefficient bounds for a new subclass of analytic bi-close-to-convex functions by making use of Faber polynomial expansion

“…If we take λ = 0 in Theorem 2.1, we have Corollary 2.4, which was proved by Hamidi and Jahangiri [8]. (1 − β)(3 − 2β); 1 2 ≤ β < 1.…”

“…In particular, for λ = 0, we have T Σ (0, β), which was introduced by Hamidi and Jahangiri [8] and they said that the bi-close-to-convex functions considered in their paper are the largest subclass of bi-univalent functions.…”

“…Only a few papers determine general coefficient bounds |a n | for the analytic bi-close-to-convex functions in the associated documents. In particular, in [8] Hamidi and Jahangiri introduced the class of bi-close-to-convex functions and determined estimates for the general coefficient |a n | of bi-close-to-convex function under certain gap series condition by using Faber polynomials.…”

Second Hankel determinant for certain subclasses ofbi-univalent functions

“…In particular, several results on coefficient estimates for the initial coefficients |a 2 |, |a 3 |, and |a 4 | were proved for various subclasses of σ (see, for example, [1,4,5,10,12,14,16,25,28,29,32,33]). …”