scholarly journals The Pre-Schwarzian Norm Estimate for Analytic Concave Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Young Jae Sim ◽  
Oh Sang Kwon
Keyword(s):  
Unit Disk ◽  
Hypergeometric Functions ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Open Unit ◽  
Opening Angle ◽  
Sufficient Condition ◽  
Open Unit Disk ◽  
Concave Functions ◽  
Norm Estimate

LetDdenote the open unit disk and letSdenote the class of normalized univalent functions which are analytic inD. LetCo(α)be the class of concave functionsf∈S, which have the condition that the opening angle off(D)at infinity is less than or equal toπα,α∈(1,2]. In this paper, we find a sufficient condition for the Gaussian hypergeometric functions to be in the classCo(α). And we define a classCo(α,A,B),(-1≤B<A≤1), which is a subclass ofCo(α)and we find the set of variabilities for the functional(1-|z|2)(f″(z)/f′(z))forf∈Co(α,A,B). This gives sharp upper and lower estimates for the pre-Schwarzian norm of functions inCo(α,A,B). We also give a characterization for functions inCo(α,A,B)in terms of Hadamard product.

scholarly journals Coefficient Estimates for a New Subclass of Analytic and Bi-Univalent Functions Defined by Hadamard Product

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Serap Bulut
Keyword(s):  
Unit Disk ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

We introduce and investigate a new general subclass ℋΣλ,μ(φ;Θ) of analytic and bi-univalent functions in the open unit disk U. For functions belonging to this class, we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|.

scholarly journals On Certain Sufficient Condition Involving Gaussian Hypergeometric Functions

2009 ◽  
Vol 2009 ◽  
pp. 1-15
Author(s):  
H. Silverman ◽  
Thomas Rosy ◽  
S. Kavitha
Keyword(s):  
Unit Disk ◽  
Hypergeometric Functions ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disk ◽  
New Class ◽  
Inclusion Properties ◽  
Complex Order ◽  
Gaussian Hypergeometric Functions

The authors define a new subclass of of functions involving complex order in the open unit disk . For this new class, we obtain certain inclusion properties involving the Gaussian hypergeometric functions.

scholarly journals Coefficient estimates for a new subclass of analytic and bi-univalent functions by Hadamard product

2021 ◽  
Vol 39 (2) ◽  
pp. 87-104
Author(s):  
Ebrahim Analouei Adegani ◽  
Ahmad Zireh ◽  
Mostafa Jafari
Keyword(s):  
Unit Disk ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In this work, we introduce a new subclas of bi-univalent functions which is defined by Hadamard product andsubordination in the open unit disk. and find upper bounds for the second and third coefficients for functions in this new subclass. Further, we generalize and improve some of the previously published results.

scholarly journals Inequalities of harmonic univalent functions with connections of hypergeometric functions

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Janusz Sokół ◽  
Rabha W. Ibrahim ◽  
M. Z. Ahmad ◽  
Hiba F. Al-Janaby
Keyword(s):  
Unit Disk ◽  
Hypergeometric Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Distortion Bounds ◽  
Class Of Functions

AbstractLet SH be the class of functions f = h+g that are harmonic univalent and sense-preserving in the open unit disk U = { z : |z| < 1} for which f (0) = f'(0)-1=0. In this paper, we introduce and study a subclass H( α, β) of the class SH and the subclass NH( α, β) with negative coefficients. We obtain basic results involving sufficient coefficient conditions for a function in the subclass H( α, β) and we show that these conditions are also necessary for negative coefficients, distortion bounds, extreme points, convolution and convex combinations. In this paper an attempt has also been made to discuss some results that uncover some of the connections of hypergeometric functions with a subclass of harmonic univalent functions.

scholarly journals On a Subclass of Analytic and Univalent Functions with Positive Coefficients Defined by a Differential Operator

2021 ◽  
pp. 2000-2008
Author(s):  
Aqeel Ketab Al-khafaji
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Positive Coefficients ◽  
Analytic And Univalent Functions

In this paper, a differential operator is used to generate a subclass of analytic and univalent functions with positive coefficients. The studied class of the functions includes:     which is defined in the open unit disk  satisfying the following condition This leads to the study of properties such as coefficient bounds, Hadamard product, radius of close –to- convexity, inclusive properties, and (n, τ) –neighborhoods for functions belonging to our class.

scholarly journals Some Geometric Properties for an Extended Class Involving Holomorphic Functions Defined by Fractional Calculus

2020 ◽  
pp. 1136-1145
Author(s):  
Sattar Kamil Hussein ◽  
Kassim Abdulhameed Jassim
Keyword(s):  
Fractional Calculus ◽  
Unit Disk ◽  
Fractional Derivatives ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Holomorphic Functions ◽  
Distortion Theorem ◽  
Fractional Integrals ◽  
Open Unit ◽  
Open Unit Disk

The main objective of" this paper is to study a subclass of holomrphic and univalent functions with negative coefficients in the open unit disk U= defined by Hadamard Product. We obtain coefficients estimates, distortion theorem , fractional derivatives, fractional integrals, and some results.

scholarly journals Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 27
Author(s):  
Hari Mohan Srivastava ◽  
Ahmad Motamednezhad ◽  
Safa Salehian
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Expansion Method ◽  
Upper Bounds ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
The Subject ◽  
Polynomial Expansion Method

In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n≧1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.

scholarly journals A new criterion for close-to-convexity of partial sums of certain hypergeometric functions

1997 ◽  
Vol 10 (2) ◽  
pp. 197-202
Author(s):  
Massoud Jahangiri
Keyword(s):  
Unit Disk ◽  
Hypergeometric Functions ◽  
Partial Sums ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Criterion

We consider the partial sums of certain hypergeometric functions and establish conditions imposed on the locations of zeros of those polynomials in order to be close-to-convex in the open unit disk.

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

2019 ◽  
Vol 12 (02) ◽  
pp. 1950017
Author(s):  
H. Orhan ◽  
N. Magesh ◽  
V. K. Balaji
Keyword(s):  
Unit Disk ◽  
Upper Bound ◽  
Chebyshev Polynomials ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
Upper Bound Estimate

In this work, we obtain an upper bound estimate for the second Hankel determinant of a subclass [Formula: see text] of analytic bi-univalent function class [Formula: see text] which is associated with Chebyshev polynomials in the open unit disk.

scholarly journals On Some Subclasses of $m$-fold Symmetric Bi-univalent Functions associated with the Sakaguchi Type Functions

2021 ◽  
pp. 1-15
Author(s):  
Ismaila O. Ibrahim ◽  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk

In the present investigation, we introduce the subclasses $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\phi,\upsilon)$ and $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\gamma,\upsilon)$ of $m$-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the Sakaguchi type of functions and defined in the open unit disk. Further, we obtain estimates on the initial coefficients $b_{m+1}$ and $b_{2m+1}$ for the functions of these subclasses and find out connections with some of the familiar classes.

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