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.

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 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 Class of Analytic Function Related with Uniformly Convex and Janowski’s Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Akhter Rasheed ◽  
Saqib Hussain ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Open Unit ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper, we introduce a new subclass of analytic functions in open unit disc. We obtain coefficient estimates, extreme points, and distortion theorem. We also derived the radii of close-to-convexity and starlikeness for this class.

Extreme Points of the Convex set of Stochastic Maps on A C*-Algebra

1998 ◽  
Vol 01 (04) ◽  
pp. 599-609 ◽  
Author(s):  
K. R. Parthasarathy
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Convex Set ◽  
Convex Combination ◽  
Extreme Points ◽  
Bounded Operators ◽  
Completely Positive ◽  
C Algebra ◽  
Permutation Matrices ◽  
Normal Maps

Let [Formula: see text] be a unital C*-subalgebra of the C*-algebra ℬ(ℋ) of all bounded operators on a complex separable Hilbert space ℋ. Let [Formula: see text] denote the convex set of all unital, linear, completely positive and normal maps of [Formula: see text] into itself. Using Stinespring's theorem, we present a criterion for an element [Formula: see text] to be extremal. When [Formula: see text], this criterion leads to an explicit description of the set of all extreme points of [Formula: see text]. We also obtain a quantum probabilistic analogue of the classical Birkhoff's theorem2 that every bistochastic matrix can be expressed as a convex combination of permutation matrices.

scholarly journals A New Class of Analytic Functions Defined by Using Salagean Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
R. M. El-Ashwah ◽  
M. K. Aouf ◽  
A. A. M. Hassan ◽  
A. H. Hassan
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Integral Means ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Fractional Calculus Operators

We derive some results for a new class of analytic functions defined by using Salagean operator. We give some properties of functions in this class and obtain numerous sharp results including for example, coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, integral means inequalities, and partial sums of functions belonging to this class. Finally, we give an application involving certain fractional calculus operators that are also considered.

scholarly journals A New Subclass of Analytic Functions Defined by Using Salagean q-Differential Operator

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 458 ◽  
Author(s):  
Muhammad Naeem ◽  
Saqib Hussain ◽  
Tahir Mahmood ◽  
Shahid Khan ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Coefficient Estimates ◽  
Quantum Calculus

In our present investigation, we use the technique of convolution and quantum calculus to study the Salagean q-differential operator. By using this operator and the concept of the Janowski function, we define certain new classes of analytic functions. Some properties of these classes are discussed, and numerous sharp results such as coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, and integral mean inequalities of functions belonging to these classes are obtained and studied.

Generalized Bloch Mappings in Complex Hilbert Space

1977 ◽  
Vol 29 (2) ◽  
pp. 299-306 ◽  
Author(s):  
Fletcher D. Wicker
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Unit Disc ◽  
Bloch Function ◽  
Complex Hilbert Space ◽  
Function Concept ◽  
Bounded Analytic Functions ◽  
Bloch Functions ◽  
Normal Functions ◽  
The Family

Anderson, Clunie and Pommerenke defined and studied the family of Bloch functions on the unit disc (see [1]). This family strictly contains the space of bounded analytic functions. However, all Bloch functions are normal and therefore enjoy the “nice” properties of normal functions. The importance of the Bloch function concept is the combination of their richness as a family and their “nice” behavior.

scholarly journals Applications of Borel Distribution Series on Analytic Functions

2020 ◽  
pp. 71-82
Author(s):  
Abbas Kareem Wanas ◽  
Jubran Abdulameer Khuttar
Keyword(s):  
Power Series ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Sigma Delta ◽  
The Family ◽  
Necessary And Sufficient

The purpose of the present paper is to determine the necessary and sufficient conditions for the power series B_{\mu} whose coefficients are probabilities of the Borel distribution to be in the family H(\lambda, \sigma, \delta, \mu) of analytic functions which defined in the open unit disk. We derive a number of important geometric properties, such as, coefficient estimates, integral representation, radii of starlikeness and convexity. Also we discuss the extreme points and neighborhood property for functions belongs to this family.

Fidelity, sub-fidelity, super-fidelity and their preservers

2015 ◽  
Vol 13 (03) ◽  
pp. 1550027
Author(s):  
Li Wang ◽  
Jinchuan Hou ◽  
Kan He
Keyword(s):  
Hilbert Space ◽  
Unitary Operator ◽  
Convex Set ◽  
Quantum Systems ◽  
Complex Hilbert Space ◽  
Quantum States ◽  
Infinite Dimensional

Sub- and super-fidelity describe respectively the lower and super bound of fidelity of quantum states. In this paper, we obtain several properties of sub- and super-fidelity for both finite- and infinite-dimensional quantum systems. Furthermore, let H be a separable complex Hilbert space and ϕ : 𝒮(H) → 𝒮(H) a map, where 𝒮(H) denotes the convex set of all states on H. We show that, if dim H < ∞, or, if dim H = ∞ and ϕ is surjective, then the following statements are equivalent: (1) ϕ preserves the super-fidelity; (2) ϕ preserves the fidelity; (3) ϕ preserves the sub-fidelity; (4) there exists a unitary or an anti-unitary operator U on H such that ϕ(ρ) = UρU† for all ρ ∈ 𝒮(H).

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