Fekete-Szego problem for certain subclass of quasi-convex functions

Abstract

For 0 ≤ α < 1, let Q α be the class of functions f which are normalised analytic and univalent in D = {z : |z| < 1} satisfying the conditionwhere g is a normalised convex function. For f ∈ Q α , sharp bounds are obtained for the Feketo-Szegö functional |a 3 − μa 2 2 | when μ is real. Mathematics Subject Classification: Primary 30C45

Faber polynomial coefficient estimates for bi-quasi-convex functions

“…Note that, by using Lemma 2.1, we have |c n | ≤ 2 and |d n | ≤ 2. Compare the coefficient of equation 7and 9, for any n ≥ 2, yields: (11) same for equation (8) and (10), we obtain:…”

“…There are many mathematicians found bounds for several subclasses of bi-univalent functions. Motivated by the work of Janteng et al [8] and recent publications ( [7] and [10]) which are applying Faber polynomial, we consider the following subclasses of bi-quasi-convex functions of the function class Σ.…”

Sharp coefficients bounds for Starlike functions associated with Gregory coefficients

“…The second Hankel determinant H 2 (2) is given by H 2 (2) := a 2 a 4 − a 2 3 . The bounds for the second Hankel determinant H 2 (2) obtained for the class S * in [21]. Lee et al [27] established the sharp bound to |H 2 (2)| by generalizing their classes using subordination.…”

Second Hankel Determinant of Bi-univalent Functions

“…There are many findings related to the results of 𝐻 2 (1), 𝐻 2 (2) and 𝐻 2 (3) for subclasses of univalent and bi-univalent functions have been widely explored by mathematicians, among them are as [5,8,10,13,17,18,20,23].…”