Geometric properties for a family of holomorphic functions associated with Wanas operator defined on complex Hilbert space

2020 ◽  
pp. 2150122
Author(s):  
Abbas Karem Wanas ◽  
Junesang Choi ◽  
Nak Eun Cho
Keyword(s):  
Hilbert Space ◽  
Extreme Points ◽  
Holomorphic Functions ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties

By making use of Wanas operator, we aim to introduce and investigate a certain family of univalent holomorphic functions with negative coefficients defined on complex Hilbert space. We present some important geometric properties of this family such as coefficient estimates, convexity, distortion and growth, radii of starlikeness and convexity. We also discuss the extreme points for functions belonging to this family.

scholarly journals A Certain Subclass of Multivalent Analytic Functions with Negative Coefficients for Operator on Hilbert Space

2019 ◽  
pp. 355-364
Author(s):  
Asraa Abdul Jaleel Husien
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties

In the present work, we introduce and study a certain subclass for multivalent analytic functions with negative coefficients defined on complex Hilbert space. We establish a number of geometric properties, like, coefficient estimates, convex set, extreme points and radii of starlikeness and convexity.

scholarly journals New Family of Multivalent Analytic Functions Defined on Complex Hilbert Space

2020 ◽  
pp. 155-165 ◽  
Author(s):  
Abbas Kareem Wanas ◽  
S. R. Swamy
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class ◽  
New Family

In this article, we define a certain new class of multivalent analytic functions with negative coefficients on complex Hilbert space. We derive a number of important geometric properties, such as, coefficient estimates, radii of starlikeness and convexity, extreme points and convex set.

scholarly journals On the Generalization of a Class of Harmonic Univalent Functions Defined by Differential Operator

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 312
Author(s):  
Aqeel Ketab AL-khafaji ◽  
Waggas Galib Atshan ◽  
Salwa Salman Abed
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class

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.

scholarly journals Some Geometric Properties Of Multivalent Convex Function For Operator On Hilbert Space

2018 ◽  
Vol 26 (8) ◽  
pp. 60-67
Author(s):  
Mohammed Hadi Lafta ◽  
Mazin Hashim Suhhiem
Keyword(s):  
Hilbert Space ◽  
Convex Function ◽  
Convex Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Weighted Mean ◽  
Geometric Properties ◽  
Closure Theorem ◽  
Coefficient Inequality

              By making use of the operator on Hilbert space, we introduce and study some properties of geometric of a subclass of multivalent convex functions with negative coefficients. Also, we obtain some geometric properties, such as coefficient inequality, growth and distortion theorem, extreme points, convex set, closure theorem, radius of close-to-convexity, weighted mean and inclusive properties.

scholarly journals A Class of Harmonic Univalent Functions Defined by Differential Operator and the Generalization

2020 ◽  
pp. 1440-1445
Author(s):  
Faten Fakher Aubdulnabi ◽  
Kassim A. Jassim
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class

In this paper, a new class of harmonic univalent functions was defined by the differential operator. We obtained some geometric properties, such as the coefficient estimates, convex combination, extreme points, and convolution (Hadamard product), which are required

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 Lipschitz-Type and Bloch-Type Spaces of Pluriharmonic Mappings in a Hilbert Space

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Yong Liu
Keyword(s):  
Hilbert Space ◽  
Holomorphic Functions ◽  
Complex Hilbert Space ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Infinite Dimensional ◽  
Type Spaces

We investigate some properties of pluriharmonic mappings in an infinite dimensional complex Hilbert space. Several characterizations for pluriharmonic mappings to be in Lipschitz-type and Bloch-type spaces are given, which are generalizations of the corresponding known ones for holomorphic functions with several complex variables.

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