scholarly journals Applications of $ q $-difference symmetric operator in harmonic univalent functions

2021 ◽  
Vol 7 (1) ◽  
pp. 667-680
Author(s):  
Caihuan Zhang ◽  
◽  
Shahid Khan ◽  
Aftab Hussain ◽  
Nazar Khan ◽  
...  
Keyword(s):  
Differential Operator ◽  
Operator Theory ◽  
Harmonic Functions ◽  
Symmetric Operator ◽  
Univalent Functions ◽  
Coefficient Bounds ◽  
New Class ◽  
Coefficient Condition ◽  
Distortion Theorems ◽  
First Time

<abstract><p>In this paper, for the first time, we apply symmetric $ q $ -calculus operator theory to define symmetric Salagean $ q $-differential operator. We introduce a new class $ \widetilde{\mathcal{H}}_{q}^{m}\left(\alpha \right) $ of harmonic univalent functions $ f $ associated with newly defined symmetric Salagean $ q $-differential operator for complex harmonic functions. A sufficient coefficient condition for the functions $ f $ to be sense preserving and univalent and in the same class is obtained. It is proved that this coefficient condition is necessary for the functions in its subclass $ \overline{\widetilde{\mathcal{H}}_{q}^{m}\left(\alpha \right) } $ and obtain sharp coefficient bounds, distortion theorems and covering results. Furthermore, we also highlight some known consequence of our main results.</p></abstract>

ON SOME PROPERTIES OF A GENERALIZED CLASS OF CLOSE-TO-STARLIKE FUNCTIONS

2019 ◽  
Vol 4 (1) ◽  
pp. 193
Author(s):  
Ajab Bai Akbarally ◽  
Nor Siti Khadijah
Keyword(s):  
Univalent Functions ◽  
Starlike Functions ◽  
Starlike Function ◽  
Coefficient Bounds ◽  
New Class ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

In this paper, we consider a new class of close-to-starlike functions  defined by the Carlson-Shaffer operator. Let denote the class of analytic univalent functions defined by then  ifsatisfy the condition  ,where  and is a starlike function. Properties  of the class  such as the coefficient bounds, growth and distortion theorems and radius properties are investigated. 

scholarly journals On Harmonic Functions Defined by Differential Operator with Respect tok-Symmetric Points

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Afaf A. Ali Abubaker ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Representation Theorem ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Distortion Theorem ◽  
Coefficient Condition ◽  
Symmetric Points

We introduce new classesMHkσ,s(λ,δ,α)andM¯Hkσ,s(λ,δ,α)of harmonic univalent functions with respect tok-symmetric points defined by differential operator. We determine a sufficient coefficient condition, representation theorem, and distortion theorem.

scholarly journals A class of harmonic functions associated with a generalized differential operator

2020 ◽  
Vol 108 (122) ◽  
pp. 145-154
Author(s):  
Sarika Verma ◽  
Deepali Khurana ◽  
Raj Kumar
Keyword(s):  
Differential Operator ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class ◽  
Inclusion Relations ◽  
Generalized Differential

We introduce a new class of harmonic univalent functions by using a generalized differential operator and investigate some of its geometric properties, like, coefficient estimates, extreme points and inclusion relations. Finally, we show that this class is invariant under Bernandi-Libera-Livingston integral for harmonic functions.

scholarly journals Certain convex harmonic functions

2002 ◽  
Vol 29 (8) ◽  
pp. 459-465 ◽  
Author(s):  
Yong Chan Kim ◽  
Jay M. Jahangiri ◽  
Jae Ho Choi
Keyword(s):  
Analytic Functions ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Uniformly Convex ◽  
Coefficient Bounds ◽  
Distortion Theorems ◽  
Harmonic Convex ◽  
Complex Valued ◽  
Convex Univalent Functions

We define and investigate a family of complex-valued harmonic convex univalent functions related to uniformly convex analytic functions. We obtain coefficient bounds, extreme points, distortion theorems, convolution and convex combinations for this family.

scholarly journals Difference formula defined by a new differential symmetric operator for a class of meromorphically multivalent functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Ibtisam Aldawish
Keyword(s):  
Differential Operator ◽  
Boundary Value Problems ◽  
Unit Disk ◽  
Spectral Theory ◽  
Analytic Functions ◽  
Special Class ◽  
Symmetric Operator ◽  
New Class ◽  
Difference Formula ◽  
Symmetric Operators

AbstractSymmetric operators have benefited in different fields not only in mathematics but also in other sciences. They appeared in the studies of boundary value problems and spectral theory. In this note, we present a new symmetric differential operator associated with a special class of meromorphically multivalent functions in the punctured unit disk. This study explores some of its geometric properties. We consider a new class of analytic functions employing the suggested symmetric differential operator.

scholarly journals Faber Polynomial Coefficient Estimates for Subclass of Analytic Bi-Bazilevic Functions Defined by Differential Operator

2019 ◽  
Vol 16 (1(Suppl.)) ◽  
pp. 0248
Author(s):  
Juma Et al.
Keyword(s):  
Differential Operator ◽  
Explicit Formula ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Faber Polynomials ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Bazilevic Functions

In this work,  an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions.          In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.  

scholarly journals Bounded Doubly Close-to-Convex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Dorina Răducanu
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Coefficient Bounds ◽  
New Class ◽  
Radius Of Convexity ◽  
Distortion Theorems

We consider a new classCC(α,β)of bounded doubly close-to-convex functions. Coefficient bounds, distortion theorems, and radius of convexity for the classCC(α,β)are investigated. A corresponding class of doubly close-to-starlike functionsS*S(α,β)is also considered.

scholarly journals On Fully-Convex Harmonic Functions and their Extension

2018 ◽  
Vol 38 (2) ◽  
pp. 51-60
Author(s):  
Shahpour Nosrati ◽  
Ahmad Zireh
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Uniformly Convex ◽  
Circular Arc ◽  
Coefficient Condition ◽  
Necessary And Sufficient ◽  
Convex Univalent Functions

‎Uniformly convex univalent functions that introduced by Goodman‎, ‎maps every circular arc contained in the open unit disk with center in it into a convex curve‎. ‎On the other hand‎, ‎a fully-convex harmonic function‎, ‎maps each subdisk $|z|=r<1$ onto a convex curve‎. ‎Here we synthesis these two ideas and introduce a family of univalent harmonic functions which are fully-convex and uniformly convex also‎. ‎In the following we will mention some examples of this subclass and obtain a necessary and sufficient conditions and finally a coefficient condition will attain with convolution‎.

scholarly journals Some Properties of Complex Harmonic Mapping

2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
E. A. Eljamal ◽  
M. Darus
Keyword(s):  
Differential Operator ◽  
Harmonic Functions ◽  
Harmonic Mapping ◽  
New Class ◽  
Generalized Differential

We introduce new class of harmonic functions by using certain generalized differential operator of harmonic. Some results which generalize problems considered by many researchers are present. The main results are concerned with the starlikeness and convexity of certain class of harmonic functions.

scholarly journals Faber Polynomial Coefficient Estimates for Subclass of Analytic Bi-Bazilevic Functions Defined by Differential Operator

2019 ◽  
Vol 16 (1) ◽  
pp. 0248
Author(s):  
Juma Et al.
Keyword(s):  
Differential Operator ◽  
Explicit Formula ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Faber Polynomials ◽  
Coefficient Estimates ◽  
Faber Polynomial ◽  
Coefficient Bounds ◽  
Bazilevic Functions

In this work,  an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions.          In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.  

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