A coefficient inequality for certain classes of analytic functions

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

“…Further Fekete and Szegö [18] introduced the generalized functional a 3 −δa 2 2 , where δ is some real number. In 1969, Keogh and Merkes [23] studied the Fekete-Szegö problem for the classes S * and K. In 2001, Srivastava et al [41] solved completely the Fekete-Szegö problem for the family C 1 := {f ∈ A : ℜ (e iη f ′ (z)) > 0, − π 2 < η < π 2 , z ∈ D} and obtained improvement of |a 3 − a 2 2 | for the smaller set C 1 . Recently, Kowalczyk et al [24] discussed the developments involving the Fekete-Szegö functional |a 3 −δa 2 2 |, where 0 ≤ δ ≤ 1 as well as the corresponding Hankel determinant for the Taylor-Maclaurin coefficients {a n } n∈N\{1} of normalized univalent functions of the form (1.1).…”

On Booth lemniscate and starlike functions

“…In order to prove next result, we need the following lemma due to Keogh and Merkes [5]. Further we denote by P the well-known class of analytic functions p(z) with p(0) = 1 and Re(p(z)) > 0, z ∈ ∆.…”

The Fekete-Szeg\"{o} Problem for a Subclass of Analytic Functions Related to Sigmoid Function

“…Several known authors at different time have applied the classical Fekete-Szegö to various classes to obtain sharp bounds. Keogh and Merkes in 1969 [4] obtained the sharp upper bound of the Fekete-Szegö functional |a 3 − µa 2 2 | for some subclasses of univalent function S. Researchers like [9], [10] and [11] studied several subclasses of functions making use of Fekete-Szegö problem and the very interesting results obtained can be found in many literature.…”