Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions

Bulut, Serap

doi:10.1016/j.crma.2014.04.004

Cited by 57 publications

(41 citation statements)

References 25 publications

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“…The problem of estimating coefficients |a n |, n ≥ 2 is still open. However, a lot of results for |a 2 |, |a 3 | and |a 4 | were proved for some subclasses of σ (see [3], [5], [9], [11], [21], [23], [24], [26], [27]). Unfortunatelly, none of them are not sharp.…”

Section: Introduction and Definitionsmentioning

confidence: 99%

Second Hankel determinant for bi-starlike and bi-convex functions of order β

Deni̇z

Çağlar

Orhan

2015

Applied Mathematics and Computation

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Abstract. In the present investigation the authors obtain upper bounds for the second Hankel determinant H 2 (2) of the classes bi-starlike and bi-convex functions of order β, represented by S * σ (β) and Kσ(β), respectively. In particular, the estimates for the second Hankel determinant H 2 (2) of bi-starlike and bi-convex functions which are important subclasses of bi-univalent functions are pointed out.

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Section: Introduction and Definitionsmentioning

confidence: 99%

Second Hankel determinant for bi-starlike and bi-convex functions of order β

Deni̇z

Çağlar

Orhan

2015

Applied Mathematics and Computation

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“…The Faber polynomials presented which play an important role in different areas of mathematical sciences, particularly in geometric function theory (Schiffer (5)). The recent interest for the calculus of Faber polynomials, particularly when it includes = −1 , the inverse of (see (10), (11), (12), (13), (14), and (15)), flawlessly fits our case for the Bi-univalent functions. As a result, we can state the following.…”

Section: )mentioning

confidence: 92%

Faber Polynomial Coefficient Estimates for Subclass of Analytic Bi-Bazilevic Functions Defined by Differential Operator

al.¹

2019

Baghdad Sci.J

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In this work, an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions. In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.

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“…Not much is known about the bounds on general coefficient | | for ≥ 4. In the literature, only few works determine general coefficient bounds | | for the analytic biunivalent functions (see [16][17][18]). The coefficient estimate problem for each of | | ( ∈ N \ {1, 2}; N = {1, 2, 3, .…”

Section: Journal Of Mathematicsmentioning

confidence: 99%