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Some properties of the class \(\mathcal{U}\)

100%

Obradovic M. , Tuneski N.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2019

tom 73

nr 1

In this paper we study the class \(\mathcal{U}\) of functions that are analytic in the open unit disk \(D =\{z : |z| < 1\}\), normalized such that\(f(0) = f'(0)-1 = 0\) and satisfy \[\left|\left[\frac{z}{f(z)}\right]^2f'(z) - 1\right|< 1\quad (z\in D).\]For functions in the class \(\mathcal{U}\) we give sharp estimates of the second and the third Hankel determinant, its relationship with the class of \(\alpha\)-convex functions, as well as certain starlike properties.

Third Hankel determinant for starlike and convex functions with respect to symmetric points

75%

Vamshee Krishna D. , Venkateswarlu B. , RamReddy T.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2016

tom 70

nr 1

The objective of this paper is to obtain best possible upper bound to the \(H_{3}(1)\) Hankel determinant for starlike and convex functions with respect to symmetric points, using Toeplitz determinants.

On the conjecture of Hayami and Owa concerning the class R(α)

75%

Zaprawa P.

Journal of Applied Analysis

2017

tom Vol. 23, nr 1

25--32

In the paperwe discuss the functional Φf(μ) ≡ a2a4 − μa23 for functions in the class R(α), α ϵ [0, 1). This class consists of analytic functions which satisfy the condition Re f’ (z) > α for all z in the unit disk Δ.We show that the conjecture of Hayami and Owa [1], that is, |Φf(μ)| ≤ (1 − α)2 · max{ 1/2 – 4/9μ, 4/9μ} for all f ϵ R(α) and μ ϵ R, is false. Moreover, we find estimates of |Φf(μ)| that improve the results obtained by Hayami and Owa.

Coefficient inequalities for a subclass of Bazilevič functions

51%

Fitri S. a. , Marjono , Thomas D. K. , Wibowo R. B. E.

Demonstratio Mathematica

2020

tom Vol. 53, nr 1

27--37

Let f be analytic in D={z:|z| < 1} with f(z)=z+∑∞n=2anzn, and for α ≥ 0 and 0 < λ ≤ 1, let B1(α,λ) denote the subclass of Bazilevič functions satisfying (…) <λ for 0 < λ ≤ 1. We give sharp bounds for various coefficient problems when f ∈ B1(α,λ), thus extending recent work in the case λ = 1.

An upper bound for third Hankel determinant of starlike functions related to shell-like curves connected with Fibonacci numbers

51%

Sokół J. , İlhan S. , Güney H. Ö.

Journal of Mathematics and Applications

2018

tom Vol. 41

195--206

We investigate the third Hankel determinant problem for some starlike functions in the open unit disc, that are related to shell-like curves and connected with Fibonacci numbers. For this, firstly, we prove a conjecture, posed in [17], for sharp upper bound of second Hankel determinant. In the sequel, we obtain another sharp coefficient bound which we apply in solving the problem of the third Hankel determinant for these functions.