# Waggas Galib AtshanUniversity of Al-Qadisiyah | UAQ · Department of Mathematics

Waggas Galib Atshan

Professor (full) Dr. in Mathematics - Complex Analysis

## About

286

Publications

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626

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Introduction

Waggas Galib Atshan currently works at the Department of Mathematics, University of Al-Qadisiyah. Waggas does research in Analysis. Their current project is 'On a Differential Subordination'.

Additional affiliations

December 2013 - February 2020

September 2013 - February 2020

## Publications

Publications (286)

We present several new results for higher-order (fourth-order) differential subordination and superordination in this paper by using the new operator Hα,β, , ,γ,nf(v) and offer numerous new findings for fourth-order differential subordination and superordination. The innovative discoveries presented here are connected to those mentioned in previous...

The goal this study is obtain some conclusions differential subordination and superordination for p-valent functions involving a differential operator. In addition, certain sandwich theorems are found.

In this paper, by making use an integral operator, we obtain third order sandwich theorems for analytic multivalent functions by using some results of differential subordination and superordination.

In the present paper, we obtain Third-Order sandwich theorems for univalent functions by using some results of differential subordination and superordination for univalent functions involving integral operator.

The main idea of this paper is to derive some modern subordination and superordination results and we obtain sandwich theorems for subclass of meromorphic univalent functions.

This paper is concerned with studying some results by introducing a new Hadamard product , , , , operator for differential subordination and superordination for certain univalent functions in the open unit disc U. Firstly, we state some basic definitions and required theorems. Furthermore. Some sandwich theorems are derived. The differential subord...

This paper is concerned with studying some results by introducing a new Hadamard
product MC,ηγ,b,v,δ operator for differential subordination and superordination for certain univalent functions in the open unit disc U. Firstly, we state some basic definitions and required theorems. Furthermore. Some sandwich theorems are derived. The differential su...

This paper is concerned with studying some results by introducing a new Hadamard
product MC,η γ,b,v,δ operator for differential subordination and superordination for certain univalent functions in the open unit disc U. Firstly, we state some basic definitions and required theorems. Furthermore. Some sandwich theorems are derived. The differential s...

In the present paper, we considered two general subclasses H Σ,m (γ, µ, λ, η; α) and H Σ,m (γ, µ, λ, η; β) of Σ m , consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U. For functions belonging to the two classes introduced here, we derived estimates on the modulus of the initial coefficients a m+1 and a 2m+1....

In this current study, we aim to give some results for third-order differential subordination and superordination for analytic functions in ∈ ℂ: | | 1 involving the generalized operator ,. The results are derived by investigating relevant classes of admissible functions. Some new results on differential subordination and superordination with some s...

A new form for the fourth Hankel determinant is given in this paper as H 4 (1) = 1 a 2 a 3 a 4 a 2 a 3 a 4 a 5 a 3 a 4 a 5 a 6 a 4 a 5 a 6 a 7 The new concept of fourth Hankel determinant is studied for the subclass of analytic functions W (δ, β, λ, t) defined here using the concept of subordination. Bounds on the coefficients |a n | with n = 2, 3,...

In the present paper, we introduce new applications on fourth-order differential subordination associated with differential linear operator I s,r,1 (n, λ) in the punctured open unit disk U *. Also, we obtain some new results.

In this research, we study suitable classes of admissible functions and establish the properties of third-order differential subordination by making use a certain differential operator of analytic functions in U and have the normalized Taylor–Maclaurin series of the form: f(z)=z+∑n=2∞anzn, (z∈U). Some new results on differential subordination with...

The purpose of the present paper is to introduce and investigate a new subclasses of analytic and bi-univalent functions defined in the open unit disk,which are associated with the quasi-subordination. We obtain estimates on the initial coefficients |a 2 | and |a 3 | of functions in these subclasses. Also several known and new consequences of these...

In the present paper, we obtain sandwich theorems for univalent functions by using some results of differential subordination and superordination for univalent functions involving the Rafid-Jassim operator.

In this paper, we give an upper bound for the fourth Hankel determinant H 4 (1) for a new class S # C associated with the sine function.

In this paper, we study some differential subordination and subordination results for certain subclass of univalent functions in the open unit disc U using generalized operator H λ,δ η,µ. Also, we derive some sandwich theorems.

In the present paper, we obtain some subordination and superordination results involving the Hadamard product operator D µ,b α,c for certain normalized analytic univalent functions in the open unit disk. These results are applied to obtain sandwich results.

In this paper, we obtain some applications of fourth-order differential subordination and superordi-nation results involving multiplier transformation H p (τ, ψ), for p-valent functions. Also, we obtain several sandwich-type results.

In the present paper, we obtain some subordination and superordination results, involving the operator T a for functions of the form f (z) = z −1 + ∞ k=1 a k z k , which are meromorphic univalent in the punctured open unit disk these results are applied to obtain sandwich results.

In the present paper ,realization new classes ℶ (, , ℎ) and ℱ ℶ (′ , ′ , ℎ) of bi-univalent functions defined in the open unit disk U and its inverse = −1 satisfying the conditions that with quasi-subordination is defined on the first two Taylor-Maclaunin series coefficients | 2 | and | 3 | for functions in the new subclasses are determined. Severa...

The third order differential sandwich results are obtained for multivalent
analytic functions in the open unit disk by using certain classes of admissible functions.
Also differential subordination and superordination results are obtained.

In this current study, we aim to give some applications on fourth-order differential subordination for p-valent meromorphic functions in the region U * = {z ∈ C : 0 < |z| < 1} = U \{0}, where U = {z ∈ C : |z| < 1} , involving the linear operator L * p f. By making use of basic concepts in theory of the fourth-order, we find new outcomes.

In this paper, we study third-order differential subordination of
univalent functions defined by differential operator. We obtain new results for thirdorder
differential subordination in the open unit disk.

In this present paper, we obtain some differential subordination and superordination results, by using generalized operators for certain subclass of analytic functions in the open unit disk. Also, we derive some sandwich results.

The main purpose of this paper is to study the differential subordination result for multivalent analytic functions. We give some applications of higher-order differential subordination results involving Hadamard product for multivalent analytic functions with generalized hypergeometric function in open unit disk. We have also discussed and studied...

The main goal of this paper is to obtain some sandwich-type results for the functions of the form: 1 1 (,) n n n f z z a z ∞ − = = + ∑ which are meromorphic univalent in the punctured open unit disk U by using new integral operator. Subject Classification: (2010) 30C45.

The main goal of this paper is to obtain some sandwich-type results for the functions of the form: 1 1 (,) n n n f z z a z ¥-= = + å which are meromorphic univalent in the punctured open unit disk U by using new integral operator. Subject Classification: (2010) 30C45.

The concept of strong differential subordination was introduces in [1],[2] by Antonio and Romaguera and developed in [4]. The object of the present paper is to investigate some inclusion relations and other interesting properties for p-valent functions defined in the open unit disk of the complex plane involving linear operator by using the princip...

In this paper, by making use the differential operator, suitable classes of admissible functions are investigated and the properties of third-order sandwich theorems for multivalent analytic function are obtained.

In the present paper, we consider two new subclasses N Σ k (µ, α, τ) and N Σ k (µ, β, τ) of Σ k consisting of analytic and k-fold symmetric bi-univalent functions defined in the open unit disc U = {z : z ∈ C and |z| < 1}. For functions belonging to the two classes introduced here, we derive their normalized forms. Furthermore, we find estimates of...

We investigate specific new subclasses of the function class Σ of bi-univalent function defined in the open unit disc, which is connected with quasi-subordination. We find estimates on the Taylor-Maclaurin coefficients |a 2 | and |a 3 | for functions in these subclasses. Already pointed out are some documented and new implications of those findings...

In this paper, by making use An operator, suitable classes of admissible
functions are investigated and the properties of third-order differential
subordination are obtained

The concept of strong differential subordination was introduces in [1], [2] by Antonio and Romaguera and developed in [4]. The object of the present paper is to investigate some inclusion relations and other interesting properties for p-valent functions defined in the open unit disk of the complex plane involving linear operator by using the princi...

In this paper, we have investigated the upper bound for the second hankel determinant for some subclasses of bi-univalent functions in open unit disc ܷ by using Chebyshev polynomials.

In the present paper, we obtain some subordination and superordination results for certain multivalent functions in the open disc U by using differential operator ࣤ ߣ,ܾ,ݏ, ݒ. Also, we derive some sandwich theorems .

The main object of this paper is to find sufficient conditions for certain normalized analytic functions to satisfy sandwich conditions. We obtain some subordination and superordination results involving by Noor-Salagean operator DI m λ,n .

The Main goal of this paper is to obtain some sandwich-type results for the functions of the form: f(z)=z^(-1)+∑_(n=1)^∞▒〖a_n z^n 〗 , which are meromorphic univalent in the punctured open unit disk U by using new integral operator.

By making use of the principle of subordination, we introduce a new class W_(p,q)^(l,k) (η,α_1,m;h) for higher-order derivatives of multivalent analytic functions associated with Dziok-Srivastava operator. We obtain some result for this class.

In this paper, we study a class of univalent functions f as defined by making
use of the generalized Ruscheweyh derivatives involving a general fractional
derivative operator.
A necessary and sufficient condition for a function to be in the class
is obtained. Also, our paper includes linear combination, integral operators
and we introduce the subcl...

In the present paper, we obtain sandwich theorems for univalent functions by using some results of differential subordination and superordination for univalent functions involving linear operator. Subject Classification: 30C45

In this paper, we study a class of univalent functions f as defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator, satisfying
{\mathop{\rm Re}\nolimits} \left\{{{{z\left({{\bf{J}}_1^{\lambda,\mu}f\left(z \right)} \right)'} \over {\left({1 - \gamma} \right){\bf{J}}_1^{\lambda,\mu}f\left(z...

In this paper, we introduce and investigate some new subclasses S γ n , q ( λ , m , ϕ ) and W x k , α ( λ , δ , ϕ ) of bi-univalent functions in the unit disk U, which satisfies the qusi-subordination condition. We obtain estimates the first two Taylor-Maclarurin coefficients | a 2 | and | a 3 |.

In this paper, we obtain some applications of second-order differential Subordination results involving a generalized integral operator for certain normalized analytic functions.

In this paper, we introduce new concept that is fourth-order differential subordination and superordination associated with linear operator for univalent analytic functions in open unit disk. Here, we extended some lemmas. Also some interesting new results are obtained.

In this paper, we introduce new concept that is fourth-order differential subordination and superordination associated with differential linear operator 𝐼𝑝(𝑛,𝜆) in open unit disk. Also, we obtain some new results.

In the present paper, we obtain some subordination and superordination results involving the differential operator 𝒲𝛼,𝛽𝑗,𝛿 for certain normalized analytic functions in the open unit disk. These results are applied to obtain sandwich results.

In the present paper, we obtain some subordination and superordination Results involving the integral operator T for certain normalized analytic functions in the open unit disk. These results are applied to obtain sandwich results.

The main idea of this paper is to derive some subordination and superordination results defined by a linear operator for multivalent functions in the open unit disk. Several sandwich-type results are also obtained.

In this paper , we introduce and investigate some new subclasses S_γ^(n,q) (λ,m,ϕ) and W_x^(k,α) (λ,δ,ϕ) of bi-univalent functions in the unit disk U, which satisfies the qusi-subordination condition. We obtain estimates the first two Taylor-Maclarurin coefficients |a_2 | and |a_3 |.

In the present paper, we obtain sandwich theorems for univalent functions by using some results of differential subordination and superordination for univalent functions involving linear operator. Subject Classification: 30C45

In the present paper, we study properties of differential subordination and superordination for univalent functions in the open unit disk U defined by a linear operator. Also, we obtain sandwich theorems for univalent functions

In the present investigation, we consider two new subclasses M Σ m (λ , μ ; α) and M Σ m (λ , μ ; β) of Σ m consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U. For functions belonging to the two classes introduced here, we derive estimates on the initial coefficients | a m+1 | and | a 2m +1 |. Several related...

The aim of this paper is to introduce a new class of multivalent prestar-like analytic functions with negative coefficients. The authors study some important geometric properties such as coefficients estimates, an integral representation and some subordination properties. Also, we obtain integral mean inequalities for the fractional integral of ord...

In this paper, we introduce and investigate two interesting subclasses R ∑ h , p ( τ , γ , δ ) and of g ∑ h , p ( μ , γ , λ ) analytic and bi-univalent functions in the unit disk U.For functions belonging to the classes R ∑ h , p ( τ , γ , δ ) and g ∑ h , p ( μ, γ, λ ) , we obtain estimates on the first two Taylor-Maclaurin coefficients |a 2 | and...

The purpose of present paper is to introduce and investigate two new subclasses () and () of analytic and m-fold symmetric bi-univalent functions in the open unit disk. Among other results belonging to these subclasses upper coefficients bounds | | and | | are obtained in this study. Certain special cases are also indicated .

In this paper, we study some differential subordination and superordination results for certain univalent functions in the open unit disc U by using a new operator. Also, we derive some sandwich theorems.

In this paper, we introduce and study a new class A^* (λ,μ,ν,η,p,ζ,τ) of meromorphic multivalent functions defined by fractional calculus operator of the punctured unit disc U^*. On this class we obtain several results like, coefficient inequality, modified Hadamard product, (N,δ)-neighborhood, partial sums, convex linear combination and integral o...

In this paper, we introduce and study a new class A^* (λ,μ,ν,η,p,ζ,τ) of meromorphic multivalent functions
defined by fractional calculus operator of the punctured unit disc U^*. On this class we obtain several results
like, coefficient inequality, modified Hadamard product, (N,δ)- neighborhood, partial sums, convex linear
combination and integral...

In this paper, we introduce and discuss a certain subclass of univalent functions in the open unit disc, we obtain some properties like coefficient estimates and results of integral means by using differential subordination.

Some properties of a class of harmonic multivalent functions defined by an integral operator are introduced, like, coefficient estimates, distortion property, extreme points, inclusion results and closure under an integral operator for this class are obtained.

In this paper , we obtain some subordination and superordination results involving the integral operator .Also,we get Differential sandwich results for classes of univalent functions in the unit disk.

In this paper, by making use of the generalized operator, we introduce and study subordination and superordination results involving Hadamard product for certain normalized analytic functions in the open unit disk. Our results extended corresponding previously known results.

In this article, a new class of harmonic univalent functions, defined by the differential
operator, is introduced. Some geometric properties, like, coefficient estimates, extreme points,convex combination and convolution (Hadamard product) are obtained.

A new class of harmonic univalent functions defined by differential operator is introduced. Some geometric properties, like, coefficient estimates, extreme points, convex combinationand convolution (Hadamard product) are obtained.

I am glad to let you know that your peer-reviewed abstract entitled: "On sandwich theorems for univalent meromorphic functions involving integral operator "

By using of linear operator, we obtain some Subordinations and superordinations results for certain normalized meromorphic univalent analytic functions in the in the punctured open unit disk Also we derive some sandwich theorems .

In the present paper, we introduce two new subclasses of the class consisting of analytic and bi-univalent functions in the open unit disk. Also, we obtain the estimates on the Taylor-Maclurin coefficients | | and | | for functions in these subclasses. We obtain new special cases for our results.

In this paper, we deduce some subordination and superordination outcomes involving the generalized differential operator í µí°· í µí¼ 1 ,í µí¼ 2 ,í µí± í µí± ,í µí± (í µí± 1 , í µí± 1) for certain multivalent analytic functions in the open unit disk. These outcomes are applied to obtain differential sandwich theorems.

The purpose of the present paper is to introduce and investigate two new subclasses of bi-univalent function of complex order defined in the open unit disk, which are associated with Srivastava-Attiya operator and satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients í µí± 2 and í µí± 3 for functio...

In this paper, we introduce and investigate a new general subclasses and of consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk We obtain estimates on the Taylor-Maclaurin coefficients | | and | | Also, we obtain new special cases for our results.

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.

In this paper we investigate and obtain on subordination results for generalized deriving function of a new class of univalent analytic functions in the open unit disk.

In the present paper, we introduce a new class of meromorphic univalent functions on the punctured unit disk U^(*)={z∈C:0<|z|<1}. We obtain some geometric properties, like, coefficient inequality, growth and distortion bounds, closure theorems, integral operator, radiiof starlikeness and convexity, extreme points, partial sums and neighborhood prop...

The in this paper, we to study the class of meromorphic univalent functions. We obtain some geometric properties, like, coefficient bounds, convex linear combinations, distortion bounds, extreme points, closure, Convexity Theorem, andneighborhood property.

In the present paper, we introduce a new class of meromorphic univalent functions on the punctured unit disk U^(*)={z∈C:0<|z|<1}. We obtain some geometric properties, like, coefficient inequality, growth and distortion bounds, closure theorems, integral operator, radiiof starlikeness and convexity, extreme points, partial sums and neighborhood prop...

## Questions

Question (1)

## Projects

Projects (5)

Using of Fick's law to find the prediction of pollution concentration in air