scholarly journals On certain classes of harmonic P-valent functions by applying the Ruscheweyh derivatives

Filomat ◽  
2009 ◽  
Vol 23 (1) ◽  
pp. 91-101 ◽  
Author(s):  
A. Ebadian ◽  
A. Tehranchi
Keyword(s):  
Unit Disk ◽  
Convex Combination ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Inclusion Relations ◽  
Coefficient Condition ◽  
Necessary And Sufficient ◽  
Complex Valued

In this paper we have introduced two new classes HRp(?, ?, k, v),HRp(?, ?, k, v) of complex valued harmonic multivalent functions of the form f = h+g, where h and g are analytic in the unit disk ? = {z: |z| < 1} and f(z) satisfying the condition Re (1-?)Df+ ?(1-k)(Df)'+ ?k(Df)''> ? A sufficient coefficient condition for this function in the class HRp(?, ?, k, v) and a necessary and sufficient coefficient condition for the function f in the class HRp(?, ?, k, v) are determined. We investigate inclusion relations, distortion theorem, extreme points, convex combination and other interesting properties for these families. .

scholarly journals A Subclass of Harmonic Univalent Functions Associated with -Analogue of Dziok-Srivastava Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Huda Aldweby ◽  
Maslina Darus
Keyword(s):  
Hypergeometric Function ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds ◽  
Basic Hypergeometric Function ◽  
Generalized Operator ◽  
Coefficient Condition ◽  
Necessary And Sufficient ◽  
Complex Valued

We study a class of complex-valued harmonic univalent functions using a generalized operator involving basic hypergeometric function. Precisely, we give a necessary and sufficient coefficient condition for functions in this class. Distortion bounds, extreme points, and neighborhood of such functions are also considered.

scholarly journals Properties of a Class of -Harmonic Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Elif Yaşar ◽  
Sibel Yalçın
Keyword(s):  
Differential Operator ◽  
Positive Integer ◽  
Harmonic Functions ◽  
Convex Combination ◽  
Extreme Points ◽  
Distortion Bounds ◽  
Harmonic Equation ◽  
Necessary And Sufficient ◽  
Complex Valued

A times continuously differentiable complex-valued function in a domain is -harmonic if satisfies the -harmonic equation , where is a positive integer. By using the generalized Salagean differential operator, we introduce a class of -harmonic functions and investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points, and convex combination of the class.

Characterization of Extreme Points of Multi-Stochastic Tensors

2016 ◽  
Vol 16 (3) ◽  
pp. 459-474 ◽  
Author(s):  
Rihuan Ke ◽  
Wen Li ◽  
Mingqing Xiao
Keyword(s):  
Operation Research ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Extreme Points ◽  
Stochastic Matrices ◽  
Third Order ◽  
New Approach ◽  
3 Dimensional ◽  
Necessary And Sufficient

AbstractStochastic matrices play an important role in the study of probability theory and statistics, and are often used in a variety of modeling problems in economics, biology and operation research. Recently, the study of tensors and their applications became a hot topic in numerical analysis and optimization. In this paper, we focus on studying stochastic tensors and, in particular, we study the extreme points of a set of multi-stochastic tensors. Two necessary and sufficient conditions for a multi-stochastic tensor to be an extreme point are established. These conditions characterize the “generators” of multi-stochastic tensors. An algorithm to search the convex combination of extreme points for an arbitrary given multi-stochastic tensor is developed. Based on our obtained results, some expression properties for third-order and n-dimensional multi-stochastic tensors (${n=3}$ and 4) are derived, and all extreme points of 3-dimensional and 4-dimensional triply-stochastic tensors can be produced in a simple way. As an application, a new approach for the partially filled square problem under the framework of multi-stochastic tensors is given.

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.

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

scholarly journals QKtype spaces of analytic functions

2006 ◽  
Vol 4 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Hasi Wulan ◽  
Jizhen Zhou
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Nondecreasing Function ◽  
Necessary And Sufficient Conditions ◽  
Type Space ◽  
Necessary And Sufficient ◽  
Spaces Of Analytic Functions

For a nondecreasing functionK:[0,8)?[0,8)and0<p<8,-2<q<8, we introduceQK(p,q), aQKtype space of functions analytic in the unit disk and study the characterizations ofQK(p,q). Necessary and sufficient conditions onKsuch thatQK(p,q)become some known spaces are given.

A New, Necessary and Sufficient Vertex Solution for Robust Stability Check of Unstructured Convex Combination Matrix Families

2015 ◽  
Author(s):  
Rama K. Yedavalli
Keyword(s):  
Robust Stability ◽  
Convex Combination ◽  
Convexity Property ◽  
Ecological Principles ◽  
Sign Structure ◽  
Previous Solution ◽  
Peer Community ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Complete Dependence

This paper revisits the problem of checking the robust stability of matrix families generated by ‘Unstructured Convex Combinations’ of user supplied or externally supplied Vertex Matrices. A previous solution given by the author for this problem involved complete dependence on the quantitative (eigenvalue information) of a set of special matrices labeled the Kronecker Nonsingularity (KN) matrices. In this solution, the ‘convexity’ property is not explicit and transparent, to the extent that, unfortunately, the accuracy of the solution itself is being questioned and not embraced by the peer community. To erase this unforunate and unwarranted image of this author (in this specific problem) in the minds of the peer community, in this paper, the author treads a new path to find a solution that brings out the convexity property in an explicit and understandable way. In the new solution presented in this paper, we combine the qualitative (sign) as well as quantitative (magnitude) information of these KN matrices and present a vertex solution in which the convexity property of the solution is transparent making it more elegant and accepatble to the peer community, than the previous solution. The new solution clearly underscores the importance of using the sign structure of a matrix in assessing the stability of a matrix. This new solution is made possible by the new insight provided by the qualitative (sign) stability/instability derived from ecological principles. Examples are given which clearly demonstrate effectiveness of the new, convexity based algorithm. It is hoped that this new solution will be embraced by the peer community.

scholarly journals On the univalency for certain subclass of analytic functions involving Ruscheweyh derivatives

2002 ◽  
Vol 31 (9) ◽  
pp. 567-575 ◽  
Author(s):  
Liu Mingsheng
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Covering Theorem ◽  
Inclusion Relations ◽  
Special Case ◽  
Class Of Functions

LetHbe the class of functionsf(z)of the formf(z)=z+∑ K=2 + ∞a k z k, which are analytic in the unit diskU={z;|z|<1}. In this paper, we introduce a new subclassBλ(μ,α,ρ)ofHand study its inclusion relations, the condition of univalency, and covering theorem. The results obtained include the related results of some authors as their special case. We also get some new results.

Some properties of a subclass of uniformly convex functions with negative coefficients

2008 ◽  
Vol 41 (2) ◽  
Author(s):  
M. K. Aouf ◽  
A. O. Mostafa
Keyword(s):  
Convex Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions

AbstractThe aim of this paper is to obtain coefficient estimates, distortion theorem, extreme points and radii of close - to - convexity, starlikeness and convexity for functions belonging to the subclass

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