Second Hankel determinant for certain subclasses ofbi-univalent functions

Abstract

In the present paper, we obtain the upper bounds for the second Hankel determinant for certain subclasses of analytic and bi-univalent functions. Moreover, several interesting applications of the results presented here are also discussed.

Second Hankel determinant for certain class of bi-univalent functions defined by Chebyshev polynomials

“…Very recently, the upper bounds of H 2 (2) for the classes S * σ (β) and K σ (β) were discussed by Deniz et al [14]. Later, the upper bounds of H 2 (2) for various subclasses of σ were obtained by Altınkaya and Yalçın [6,7], Ç aglar et al [11], Kanas et al [22] and Orhan et al [32] (see also [28,33]).…”

The Second Hankel Determinant Problem for a Class of Bi-Close-to-Convex Functions

“…for some x, y, s, t with |x| ≤ 1, |y| ≤ 1, |s| ≤ 1 and |t| ≤ 1. Applying (16) and (17) in (15), it follows that…”

“…In recent years, the research on Hankel determinants has focused on the estimation of |H 2 (2)|. Problems in this field has also been argued by several authors for various classes of univalent functions [14][15][16][17][18][19][20][21][22][23][24].…”

A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain

“…Recently, Srivastava and his coauthors [21] found the estimate of the second Hankel determinant for bi-univalent functions involving the symmetric q-derivative operator, while in [22], the authors studied Hankel and Toeplitz determinants for subfamilies of q-starlike functions connected with the conic domain. For more literature, see [23][24][25][26][27][28][29][30].…”