Bounds for the second Hankel determinant of certain bi-univalent functions

Abstract

Abstract. In the present work, we propose to investigate the second Hankel determinant inequalities for certain class of analytic and bi-univalent functions. Some interesting applications of the results presented here are also discussed. 2010 Mathematics Subject Classification: 30C45.

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]).…”

Certain classes of bi-univalent functions with bounded boundary variation

“…Various subclasses of the bi-univalent function class Σ were introduced and non-sharp estimates on the first two coefficients |a 2 | and |a 3 | in the Taylor-Maclaurin series expansion (1.1) were found in several recent investigations (see, for example, [1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,19,21,22,23,24,25,26,27,29,30,31,32,33,34,35] and references therein). The aforecited all these papers on the subject were actually motivated by the pioneering work of Srivastava et al [28].…”

The Second Hankel Determinant Problem for a Class of Bi-Univalent Functions

“…In 1976, the -th Hankel determinant was stated for integers 1 and 1 [16], as follows: where the Hankel determinant 1 is called the Fekete-Szegö functional and 2 is defined as the second Hankel determinant functional. Recently, several researchers have investigated similar problems in this direction, [18][19][20][21][22][23][24][25][26][27] to name a few. Definition 1.1.…”