scholarly journals Coefficient estimate of p-valent Bazilevic functions with a bounded positive real part

2015 ◽  
Vol 34 (2) ◽  
pp. 63-73
Author(s):  
O. S. Babu ◽  
C. Selvaraj ◽  
S. Logu ◽  
Gangadharan Murugusundaramoorthy
Keyword(s):  
Unit Disk ◽  
Positive Real Part ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimate ◽  
Positive Real ◽  
Strip Domain ◽  
Bazilevic Functions ◽  
Bounded Positive Real Part

By considering a $p-$valent Bazilevi\v{c} function in the open unit disk$\triangle$ which maps $\triangle$ onto the strip domain $w$ with$p\alpha < \Re\, w < p \beta,$ we estimate bounds of coefficients and solve Fekete-Szeg\"{o} problem forfunctions in this class.\\

scholarly journals Some characteristic properties of analytic functions

2016 ◽  
Vol 24 (1) ◽  
pp. 353-369
Author(s):  
R. K. Raina ◽  
Poonam Sharma ◽  
G. S. Sălăgean
Keyword(s):  
Convex Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Positive Real Part ◽  
Integral Representations ◽  
Open Unit ◽  
Open Unit Disk ◽  
Positive Real ◽  
Bilinear Mapping ◽  
Initial Coefficient

AbstractIn this paper, we consider a class L(λ, μ; ϕ) of analytic functions f defined in the open unit disk U satisfying the subordination condition that,where is the Sălăgean operator and ϕ(z) is a convex function with positive real part in U. We obtain some characteristic properties giving the coefficient inequality, radius and subordination results, and an inclusion result for the above class when the function ϕ(z) is a bilinear mapping in the open unit disk. For these functions f (z) ; sharp bounds for the initial coefficient and for the Fekete-Szegö functional are determined, and also some integral representations are given.

scholarly journals Generalizing Certain Analytic Functions Correlative to the n-th Coefficient of Certain Class of Bi-Univalent Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hameed Ur Rehman ◽  
Maslina Darus ◽  
Jamal Salah
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Positive Real Part ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Positive Real ◽  
Faber Polynomial ◽  
Coefficient Problems

In the present paper, the authors implement the two analytic functions with its positive real part in the open unit disk. New types of polynomials are introduced, and by using these polynomials with the Faber polynomial expansion, a formula is structured to solve certain coefficient problems. This formula is applied to a certain class of bi-univalent functions and solve the n -th term of its coefficient problems. In the last section of the article, several well-known classes are also extended to its n -th term.

scholarly journals Disk-like functions

1970 ◽  
Vol 11 (2) ◽  
pp. 251-256
Author(s):  
Richard J. Libera
Keyword(s):  
Unit Disk ◽  
Geometric Property ◽  
Starlike Functions ◽  
Positive Real Part ◽  
Open Unit ◽  
Open Unit Disk ◽  
Positive Real ◽  
Image Position

The class s of functions f(z) which are regular and univalent in the open unit disk △ = {z: |z| < 1} each normalized by the conditionshas been studied intensively for over fifty years. A large and very successful portion of this work has dealt with subclasses of L characterized by some geometric property of f[Δ], the image of Δ under f(z), which is expressible in analytic terms. The class of starlike functions in L is one of these [3]; f(z) is starlike with respect to the origin if the segment [0,f(z)] is in f[Δ] for every z in Δ and this condition is equivalent to requiring that have a positive real part in Δ.

scholarly journals Coefficient Estimate of Biunivalent Functions of Complex Order Associated with the Hohlov Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Z. Peng ◽  
G. Murugusundaramoorthy ◽  
T. Janani
Keyword(s):  
Unit Disk ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimate ◽  
Complex Order

We introduce and investigate a new subclass of the function class Σ of biunivalent functions of complex order defined in the open unit disk, which are associated with the Hohlov operator, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in this new subclass. Several, known or new, consequences of the results are also pointed out.

scholarly journals Radius of starlikeness of certain analytic functions

2021 ◽  
Vol 71 (1) ◽  
pp. 83-104
Author(s):  
Asha Sebastian ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Positive Real Part ◽  
Open Unit ◽  
Open Unit Disk ◽  
Sine Function ◽  
Positive Real ◽  
Radius Of Starlikeness ◽  
Lemniscate Of Bernoulli

Abstract This paper studies analytic functions f defined on the open unit disk of the complex plane for which f/g and (1 + z)g/z are both functions with positive real part for some analytic function g. We determine radius constants of these functions to belong to classes of strong starlike functions, starlike functions of order α, parabolic starlike functions, as well as to the classes of starlike functions associated with lemniscate of Bernoulli, cardioid, lune, reverse lemniscate, sine function, exponential function and a particular rational function. The results obtained are sharp.

scholarly journals Coefficient Estimates of Certain Subclasses of Bi-Bazilevic Functions Associated with Chebyshev Polynomials and Mittag-Leffler Function

2020 ◽  
pp. 365-376
Author(s):  
Adeniyi Musibau Gbolagade ◽  
Ibrahim Tunji Awolere
Keyword(s):  
Unit Disk ◽  
Chebyshev Polynomials ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Bazilevic Functions

In this present investigation, the authors introduced certain subclasses of the function class $ T^{\alpha}_{\theta}(\lambda, \beta, t)$ of bi-Bazilevic univalent functions defined in the open unit disk $U$, which are associated with Chebyshev polynomials and Mittag-Leffler function. We establish the Taylor Maclaurin coefficients $\left|a_{2}\right|$, $\left|a_{3}\right|$ and $\left|a_{4}\right|$ for functions in the new subclass introduced and the Fekete-Szego problem is solved.

scholarly journals Starlikeness of certain non-univalent functions

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Adam Lecko ◽  
V. Ravichandran ◽  
Asha Sebastian
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Positive Real Part ◽  
The Other ◽  
Open Unit ◽  
Sigmoid Function ◽  
Open Unit Disk ◽  
Positive Real ◽  
Lemniscate Of Bernoulli

AbstractWe consider three classes of functions defined using the class $${\mathcal {P}}$$ P of all analytic functions $$p(z)=1+cz+\cdots $$ p ( z ) = 1 + c z + ⋯ on the open unit disk having positive real part and study several radius problems for these classes. The first class consists of all normalized analytic functions f with $$f/g\in {\mathcal {P}}$$ f / g ∈ P and $$g/(zp)\in {\mathcal {P}}$$ g / ( z p ) ∈ P for some normalized analytic function g and $$p\in {\mathcal {P}}$$ p ∈ P . The second class is defined by replacing the condition $$f/g\in {\mathcal {P}}$$ f / g ∈ P by $$|(f/g)-1|<1$$ | ( f / g ) - 1 | < 1 while the other class consists of normalized analytic functions f with $$f/(zp)\in {\mathcal {P}}$$ f / ( z p ) ∈ P for some $$p\in {\mathcal {P}}$$ p ∈ P . We have determined radii so that the functions in these classes to belong to various subclasses of starlike functions. These subclasses includes the classes of starlike functions of order $$\alpha $$ α , parabolic starlike functions, as well as the classes of starlike functions associated with lemniscate of Bernoulli, reverse lemniscate, sine function, a rational function, cardioid, lune, nephroid and modified sigmoid function.

On a Subclass of Univalent Harmonic Mappings Convex in the Imaginary Direction

2020 ◽  
pp. 445-454
Author(s):  
Deepali Khurana ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Imaginary Axis ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Distortion Bounds ◽  
Univalent Harmonic Mappings

In the present article, we consider a class of univalent harmonic mappings, $\mathcal{C}_{T} = \left\{ T_{c}[f] =\frac{f+czf'}{1+c}+\overline{\frac{f-czf'}{1+c}}; \; c>0\;\right\}$ and $f$ is convex univalent in $\mathbb{D}$, whose functions map the open unit disk $\mathbb{D}$ onto a domain convex in the direction of the imaginary axis. We estimate coefficient, growth and distortion bounds for the functions of the same class.

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.

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