Second Hankel determinant for a subclass of analytic bi-univalent functions defined by subordination

Abstract

In this work with a different technique we obtain upper bounds of the functional a2a4 − a 2 3 for functions belonging to a comprehensive subclass of analytic bi-univalent functions, which is defined by subordinations in the open unit disk. Moreover, our results extend and improve some of the previously known ones.

Second Hankel Determinant for a Certain Subclass of Bi-Close to Convex Functions Defined by Kaplan

“…Extensive studies of the Hankel determinant in the theory of meromorphic functions are due to Wilson [17]; numerous applications in mathematical physics are given by Vein and Dale [18]. Recently, many authors have discussed upper bounds of the Hankel determinant and Fekete-Szegö functional for numerous subclasses of univalent functions [13,14,[19][20][21][22] and references therein. Very recently, the upper bounds of H 2 (2) for the classes S * Σ (α) and K Σ (α) were investigated by Deniz et al [23], and extended by Orhan et al [24,25].…”

New Results for Some Generalizations of Starlike and Convex Functions

“…In this section, we investigate the problem of coefficients for the second Hankel determinant problem (see [20][21][22][23][24]) for the classes ST L ðsÞ, S * Ne and similar classes. For this purpose, we need some parts of Theorems 1 and 2 of [25], as follows: Lemma 14 (see [25], Theorem 1).…”

Coefficient estimates for a subclass of analytic functions by Srivastava-Attiya operator

“…Let Σ denote the class of bi-univalent functions in U given by (1.1). Recently many researchers have introduced and investigated several interesting subclasses of the bi-univalent function class Σ and they have found non-sharp estimates on the first two Taylor-Maclaurin coefficients |a 2 | and |a 3 | and other problems, see for example, [3,2,4,5,6,7,8,10,11,13,14,15,22,23,24].…”