New concept on fourth Hankel determinant of a certain subclass of analytic functions

Bi-Univalent Problems Involving Certain New Subclasses of Generalized Multiplier Transform on Analytic Functions Associated with Modified Sigmoid Function

“…The new results presented in this paper are interesting for researchers since the coefficient estimates obtained in this work could be used in the future to investigate the Fekete-Szegö relation as well as the Hankel determinants for the newly introduced classes as seen in the previously cited papers [33,34], among others.…”

On Third-Order Differential Subordination and Superordination Properties of Analytic Functions Defined by a Generalized Operator

“…This follows easily from ( 9), the admissible condition for ψ ∈ Φ I,1 [Ω, q] in Definition 9 is equivalent to the admissible condition for ψ ∈ ψ I,1 [Ω, q] as given in Definition 5 for n = 2. Hence, by using the conditions in (20) and from Theorem 2, we obtain q(z) ≺ w(z), or, equivalently q(z) ≺ I j α,β f (z).…”

“…The current paper utilizes the techniques on the third-order differential subordination and superordination outcomes of Antonino and Miller [7], Ali et al [18] and Tang et al [9], respectively and different conditions (see [19,20]). Certain classes of admissible functions are investigated in this current paper, some properties of the third-order differential subordination and superordination for analytic functions in U related to the operator I j α,β f are also mentioned.…”

“…Let φ ∈ Φ I,1 [h, q] and assume h is analytic in U. If the functions f ∈ A(n) and I j α,β f (z) ∈ Q 0 fulfill the condition (20) and…”

Hankel Determinants and Coefficient Estimates for Starlike Functions Related to Symmetric Booth Lemniscate

“…Recently, sharp bounds for |H 3 (1)( f )| were obtained using a result from [31]; see [32][33][34][35][36][37] for some detailed work on Hankel determinants. A new form for the fourth Hankel determinant is given in [38], which is studied for a new subclass of analytic functions introduced, and the upper bound of the fourth Hankel determinant for this class is obtained. A new class of analytic functions associated with exponential functions is introduced in [39] and the upper bound of the third Hankel determinant is found.…”