Sharp upper and lower bounds of the Hermitian Toeplitz determinants of the second and third orders are found for various subclasses of close-to-convex functions.
Sharp upper and lower bounds of the Hermitian Toeplitz determinants of the second and third orders are found for various subclasses of close-to-convex functions.
Given a starlike function g is an element of S*, an analytic standardly normalized function f in the unit disk D is called close-to-convex with respect to g if there exists delta is an element of (-pi/2, pi/2) such th...
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Given a starlike function g is an element of S*, an analytic standardly normalized function f in the unit disk D is called close-to-convex with respect to g if there exists delta is an element of (-pi/2, pi/2) such that Re{e(i delta)zf'(z)/g(z)} > 0, z is an element of D. For the class C(h) of all close-to-convex functions with respect to h(z) := z/(1 - z), z is an element of D, a Fekete-Szego problem is examined.
We consider a subclass of the class of close-to-convex functions. We show the relationship between our class and the appropriate subordination. Moreover, we give the coefficient estimates and a sufficient condition fo...
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We consider a subclass of the class of close-to-convex functions. We show the relationship between our class and the appropriate subordination. Moreover, we give the coefficient estimates and a sufficient condition for functions to belong to the class investigated. Finally, we obtain the distortion and the growth theorems. The results presented are a generalization of the results obtained by Gao and Zhou. (C) 2010 Elsevier Ltd. All rights reserved.
Given α∈[0, 1], let hα（z） ：= z/（1 - αz）, z ∈ D ：= {z ∈ C： ｜z｜ 〈 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ （-π/2, π/2）...
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Given α∈[0, 1], let hα（z） ：= z/（1 - αz）, z ∈ D ：= {z ∈ C： ｜z｜ 〈 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ （-π/2, π/2） such that Re{e^iδ zf′（z）/hα（z）} 〉 0, z ∈ D. For the class l（hα） of all close-to-convex functions with respect to hα, the Fekete-Szego problem is studied.
Let be the elliptical domain Let denote the class of functions F analytic and univalent in satisfying the normalization conditions and In this paper, we obtain sharp bounds for the Faber coefficients of functions whic...
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Let be the elliptical domain Let denote the class of functions F analytic and univalent in satisfying the normalization conditions and In this paper, we obtain sharp bounds for the Faber coefficients of functions which belong to certain subclasses of
In this paper, bounds are established for the second Hankel determinant of logarithmic coefficients for normalised analytic functions satisfying certain differential inequality.
In this paper, bounds are established for the second Hankel determinant of logarithmic coefficients for normalised analytic functions satisfying certain differential inequality.
Some results are presented relating to questions raised in a recent paper by Anderson, Hayman and Pommerenke regarding the size of the set of boundary points of the unit disc at which a univalent function has a prescr...
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Some results are presented relating to questions raised in a recent paper by Anderson, Hayman and Pommerenke regarding the size of the set of boundary points of the unit disc at which a univalent function has a prescribed radial growth.
In this paper, we answer the questions raised in the paper [On the difference of inverse coefficients of univalent functions, Symmetry, 2020, 12(12), art. 2040, 14pp] by Sim and Thomas, and aim to verify the conjectur...
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In this paper, we answer the questions raised in the paper [On the difference of inverse coefficients of univalent functions, Symmetry, 2020, 12(12), art. 2040, 14pp] by Sim and Thomas, and aim to verify the conjecture posed therein in certain cases. For this purpose, we investigate sharp bounds on moduli difference of successive inverse coefficients for certain classes of close-to-convex functions.
Given alpha epsilon [0, 1], let g(alpha)(z) := z/(1 - alpha z)(2), z epsilon D := {z epsilon C : vertical bar z vertical bar 0, z epsilon D. For the class C(g(alpha)) of all close-to-convex functions with respect to ...
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Given alpha epsilon [0, 1], let g(alpha)(z) := z/(1 - alpha z)(2), z epsilon D := {z epsilon C : vertical bar z vertical bar < 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to g(alpha) if there exists delta epsilon (-pi/2,pi/2) such that Re {e(i delta)zf'(z)/g(alpha)(z)} > 0, z epsilon D. For the class C(g(alpha)) of all close-to-convex functions with respect to g(alpha), the Fekete-Szego problem is studied.
Abstract: Let $f(z) = \sum \nolimits _1^\infty {{a_n}} {z^n}$ be close-to-convex on the unit disc. It is shown that (a) if $\lambda > 0$, then f belongs to the Hardy space ${H^\lambda }$ if and only if ...
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Abstract: Let $f(z) = \sum \nolimits _1^\infty {{a_n}} {z^n}$ be close-to-convex on the unit disc. It is shown that (a) if $\lambda > 0$, then f belongs to the Hardy space ${H^\lambda }$ if and only if ${\sum {{n^{\lambda - 2}}\left | {{a_n}} \right |} ^\lambda }$ is finite and that (b) if $0 < \lambda < 1$, then $f’ \in {H^\lambda }$ if and only if either $\sum {{n^{2\lambda - 2}}} {\left | {{a_n}} \right |^\lambda }$ or, equivalently, $\int _0^1 {{M^\lambda }(r,f’)} dr$ is convergent. It is noted that the first of these results does not extend to the full class of univalent functions and that the second is best possible in a number of different senses.
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