SOME NEW RESULTS ASSOCIATED WITH CARATHÉODORY FUNCTIONS OF ORDER α

2016 ◽  
Vol 2 (1) ◽  
pp. 11-13
Author(s):  
H. M. Srivastava ◽  
Shigeyoshi Owa
Keyword(s):  
Unit Disk ◽  
Extremal Function ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
Carathéodory Functions ◽  
Coefficient Inequalities ◽  
The Extremal Function ◽  
Class Of Functions

Let $\mathcal{P}(\alpha)$ be the class of functions $p(z)$ which are Carathéodory functions of order $\alpha$ $(0 \le\alpha<1)$ in the open unit disk $\mathbf{U}$. Considering the extremal function $p(z)$ for the class $\mathcal{P}(\alpha)$, a new class ${\mathcal P}^*(\beta)$ $\beta\in \mathbb{R}$ of functions $q(z)$ in $\mathbf{U}$ is defined. The object of the present paper is to develop several interesting coefficient inequalities for the functions $q(z)$ in the new class $\mathcal{P}^*(\beta)$ introduced here.

New classes of certain analytic functions concerned with subordinations

2017 ◽  
Vol 33 (2) ◽  
pp. 153-160
Author(s):  
NICOLETA BREAZ ◽  
◽  
SHIGEYOSHI OWA ◽  
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Extremal Function ◽  
Open Unit ◽  
Open Unit Disk ◽  
The Extremal Function

Let A be the class of analytic functions f(z) in the open unit disk U which satisfy f(0) = 0 and f 0(0) = 1. Applying the extremal function for the subclass S∗(α) of A, new classes P∗(α) and Q∗(α) are considered using certain subordinations. The object of the present paper is to discuss some interesting properties for f(z) belonging to the classes P∗(α) and Q∗(α)

scholarly journals A Generalized Class of Functions Defined by the q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2361
Author(s):  
Loriana Andrei ◽  
Vasile-Aurel Caus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
The Relationship ◽  
Class Of Functions

The goal of the present investigation is to introduce a new class of analytic functions (Kt,q), defined in the open unit disk, by means of the q-difference operator, which may have symmetric or assymetric properties, and to establish the relationship between the new defined class and appropriate subordination. We derived relationships of this class and obtained sufficient conditions for an analytic function to be Kt,q. Finally, in the concluding section, we have taken the decision to restate the clearly-proved fact that any attempt to create the rather simple (p,q)-variations of the results, which we have provided in this paper, will be a rather inconsequential and trivial work, simply because the added parameter p is obviously redundant.

scholarly journals Convolutions of prestarlike functions

1983 ◽  
Vol 6 (1) ◽  
pp. 59-68 ◽  
Author(s):  
O. P. Ahuja ◽  
H. Silverman
Keyword(s):  
Unit Disk ◽  
Extremal Function ◽  
Extreme Points ◽  
Distortion Theorems ◽  
The Extremal Function ◽  
Class Of Functions

The convolution of two functionsf(z)=∑n=0∞anznandg(z)=∑n=0∞bnzndefined as(f∗g)(z)=∑n=0∞anbnzn. Forf(z)=z−∑n=2∞anznandg(z)=z/(1−z)2(1−γ), the extremal function for the class of functions starlike of orderγ, we investigate functionsh, whereh(z)=(f∗g)(z), which satisfy the inequality|(zh′/h)−1|/|(zh′/h)+(1-2α)|<β,0≤α<1,0<β≤1for allzin the unit disk. Such functionsfare said to beγ-prestarlike of orderαand typeβ. We characterize this family in terms of its coefficients, and then determine extreme points, distortion theorems, and radii of univalence, starlikeness, and convexity. All results are sharp.

scholarly journals On coefficient inequalities of certain subclasses of bi-univalent functions involving the Sălăgean operator

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1305-1313
Author(s):  
Amol Patil ◽  
Uday Naik
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Coefficient Inequalities

In the present investigation, with motivation from the pioneering work of Srivastava et al. [28], which in recent years actually revived the study of analytic and bi-univalent functions, we introduce the subclasses T*?(n,?) and T?(n,?) of analytic and bi-univalent function class ? defined in the open unit disk U = {z ? C : |z| < 1g and involving the S?l?gean derivative operator Dn. Moreover, we derive estimates on the initial coefficients |a2| and |a3| for functions in these subclasses and pointed out connections with some earlier known results.

scholarly journals Some general coefficient estimates for a new class of analytic and bi-univalent functions defined by a linear combination

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1313-1322 ◽  
Author(s):  
H.M. Srivastava ◽  
Müge Sakar ◽  
Güney Özlem
Keyword(s):  
Linear Combination ◽  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Faber Polynomials ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
New Class

In the present paper, we introduce and investigate a new class of analytic and bi-univalent functions f (z) in the open unit disk U. For this purpose, we make use of a linear combination of the following three functions: f(z)/z, f'(z) and z f''(z) for a function belonging to the normalized univalent function class S. By applying the technique involving the Faber polynomials, we determine estimates for the general Taylor-Maclaurin coefficient of functions belonging to the analytic and bi-univalent function class which we have introduced here. We also demonstrate the not-too-obvious behaviour of the first two Taylor-Maclaurin coefficients of such functions.

scholarly journals Argument and Coefficient Estimates for Certain Analytic Functions

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 88 ◽  
Author(s):  
Davood Alimohammadi ◽  
Nak Eun Cho ◽  
Ebrahim Analouei Adegani ◽  
Ahmad Motamednezhad
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Sharp Bounds ◽  
New Class ◽  
Logarithmic Coefficients

The aim of the present paper is to introduce a new class G α , δ of analytic functions in the open unit disk and to study some properties associated with strong starlikeness and close-to-convexity for the class G α , δ . We also consider sharp bounds of logarithmic coefficients and Fekete-Szegö functionals belonging to the class G α , δ . Moreover, we provide some topics related to the results reported here that are relevant to outcomes presented in earlier research.

scholarly journals On a subclass of close-to-convex harmonic mappings

2020 ◽  
pp. 2150102
Author(s):  
Rajbala ◽  
Jugal K. Prajapat
Keyword(s):  
Unit Disk ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Basic Properties ◽  
New Class ◽  
Radius Of Convexity

In this paper, we introduce a new class of sense preserving harmonic mappings [Formula: see text] in the open unit disk and prove that functions in this class are close-to-convex. We give some basic properties such as coefficient bounds, growth estimates, convolution and determine the radius of convexity for the sections of functions belonging to this family. In addition, we construct certain harmonic univalent polynomials belonging to this family.

scholarly journals A subclass of close-to-convex functions

2013 ◽  
Vol 44 (1) ◽  
pp. 83-89
Author(s):  
Zheng- Lv Zhang ◽  
Qing- Hua Xu
Keyword(s):  
Convex Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Distortion Theorem ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Inequalities

In this paper, we introduce and investigate an interesting subclass $\mathcal {J}_\alpha(h)$ of analytic and close-to-convex function in the open unit disk D. several coefficient inequalities, growth, and distortion theorem for this class are proved. The various results presented here would generalize many know results.

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 Generalized Briot-Bouquet differential equation based on new differential operator with complex connections

2020 ◽  
Vol 28 (1) ◽  
pp. 105-114
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Difference Operator ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
Generalized Operator ◽  
Generalized Differential

AbstractInequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.

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