Second Hankel determinant for certain class of bi-univalent functions defined by Chebyshev polynomials (original) (raw)

Second Hankel determinant for certain subclass of bi-univalent functions

Filomat, 2021

The main purpose of this paper is to obtain an upper bound for the second Hankel determinant for functions belonging to a subclass of bi-univalent functions in the open unit disk in the complex plane. Furthermore, the presented results in this work improve or generalize the recent works of other authors.

Third Hankel Determinant for a Class of Analytic Univalent Functions

2017

Let A denote the class of all normalized analytic function f in the unit disc U of the form f(z) = z + ∑∞ n=2 anz n. The objective of this paper is to obtain an upper bound to the third Hankel determinant denoted by H3(1) for certain subclass of univalent functions, using Toeplitz determinants.

Second Hankel determinant problem for a certain subclass of univalent functions

International Journal of Mathematical Analysis, 2015

Let S denote the class of analytic and univalent functions in the open unit disk D = {z : |z| < 1} with the normalization conditions. In the present artical an upper bound for the second Hankel determinant a 2 a 4 − a 2 3 is obtained for a certain subclass of univalent functions.

Bounds for the second Hankel determinant of certain univalent functions

Journal of Inequalities and Applications, 2013

The estimates for the second Hankel determinant a 2 a 4-a 2 3 of the analytic function f (z) = z + a 2 z 2 + a 3 z 3 + • • • , for which either zf (z)/f (z) or 1 + zf (z)/f (z) is subordinate to a certain analytic function, are investigated. The estimates for the Hankel determinant for two other classes are also obtained. In particular, the estimates for the Hankel determinant of strongly starlike, parabolic starlike and lemniscate starlike functions are obtained. MSC: 30C45; 30C80 H q (n) < Kn-(  +β)q+  

Second Hankel Determinant for the Subclass of Bi-Univalent Functions Using q-Chebyshev Polynomial and Hohlov Operator

Fractal and Fractional

The q-derivative and Hohlov operators have seen much use in recent years. First, numerous well-known principles of the q-derivative operator are highlighted and explained in this research. We then build a novel subclass of analytic and bi-univalent functions using the Hohlov operator and certain q-Chebyshev polynomials. A number of coefficient bounds, as well as the Fekete–Szegö inequalities and the second Hankel determinant are provided for these newly specified function classes.

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

Journal of Mathematical and Fundamental Sciences

Hankel matrices are related to a wide range of disparate determinant computations and algorithms and some very attractive computational properties are allocated to them. Also, the Hankel determinants are crucial factors in the research of singularities and power series with integral coefficients. It is specified that the Fekete-Szegö functional and the second Hankel determinant are equivalent to 2 and 2 , respectively. In this study, the upper bounds were obtained for the second Hankel determinant of the subclass of bi-univalent functions, which is defined by subordination. It is worth noticing that the bounds rendered in the present paper generalize and modify some previous results.