scholarly journals A Study of New Class of Star-Like Functions Associated by Symmetric p , q -Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Khalid Akbar ◽  
Rashid Murtaza ◽  
Adnan ◽  
Umar Khan ◽  
Ilyas Khan ◽  
...  
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Quantum Calculus ◽  
New Class ◽  
Different Parts

As of late quantum calculus is broadly utilized in different parts of mathematics. Uniquely, the hypothesis of univalent functions can be newly portrayed by utilizing q -calculus. In this paper, we utilize our recently presented symmetric p , q -number m ˜   p , q to characterize new symmetric p , q -derivative D   p , q of analytic function f in the open unit disk U . Utilizing D   p , q , we introduce new class of analytic star-like functions and examine some fascinating results.

scholarly journals CERTAIN CLASSES OF BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER ASSOCIATED WITH QUASI-SUBORDINATION INVOLVING (p, q) -DERIVATIVE OPERATOR

2020 ◽  
Vol 44 (4) ◽  
pp. 639-649
Author(s):  
S. ALTıNKAYA ◽  
S. YALçıN
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Quantum Calculus ◽  
New Class ◽  
Complex Order

In this present paper, as applications of the post-quantum calculus known as the (p,q)-calculus, we construct a new class Dp,qk(γ, ζ,Ψ ) of bi-univalent functions of complex order defined in the open unit disk. Coefficients inequalities and several special consequences of the results are obtained.

Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
S. P. Goyal ◽  
Rakesh Kumar
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

AbstractIn the present paper, we obtain the estimates on initial coefficients of normalized analytic function f in the open unit disk with f and its inverse g = f

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 Initial Coefficients of Biunivalent Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
See Keong Lee ◽  
V. Ravichandran ◽  
Shamani Supramaniam
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Special Cases

An analytic functionfdefined on the open unit disk is biunivalent if the functionfand its inversef-1are univalent in𝔻. Estimates for the initial coefficients of biunivalent functionsfare investigated whenfandf-1, respectively, belong to some subclasses of univalent functions. Some earlier results are shown to be special cases of our results.

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.

A New Subclass of Harmonic Univalent Functions

2017 ◽  
Vol 9 (2) ◽  
pp. 26-32
Author(s):  
Waggas Galib Atshan ◽  
Najah Ali Jiben Al-Ziadi
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Basic Properties ◽  
New Class

In this paper, we define a new class of harmonic univalent functions of the form  in the open unit disk . We obtain basic properties, like, coefficient bounds, extreme points, convex combination, distortion and growth theorems and integral operator.

scholarly journals Fekete-Szegö Problems for Quasi-Subordination Classes

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Maisarah Haji Mohd ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk

An analytic functionfis quasi-subordinate to an analytic functiong, in the open unit disk if there exist analytic functionsφandw, with|φ(z)|≤1,w(0)=0and|w(z)|<1such thatf(z)=φ(z)g(w(z)). Certain subclasses of analytic univalent functions associated with quasi-subordination are defined and the bounds for the Fekete-Szegö coefficient functional|a3-μa22|for functions belonging to these subclasses are derived.

scholarly journals On a Length Problem for Univalent Functions

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 266 ◽  
Author(s):  
Mamoru Nunokawa ◽  
Janusz Sokół ◽  
Nak Cho
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk

Let g be an analytic function with the normalization in the open unit disk. Let L ( r ) be the length of g ( { z : | z | = r } ) . In this paper we present a correspondence between g and L ( r ) for the case when g is not necessary univalent. Furthermore, some other results related to the length of analytic functions are also discussed.

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 On the Fekete-Szegö problem

2000 ◽  
Vol 24 (9) ◽  
pp. 577-581 ◽  
Author(s):  
B. A. Frasin ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Upper Bound ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Strongly Starlike Functions ◽  
Strongly Starlike

Letf(z)=z+a2z2+a3z3+⋯be an analytic function in the open unit disk. A sharp upper bound is obtained for|a3−μa22|by using the classes of strongly starlike functions of orderβand typeαwhenμ≥1.

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