scholarly journals Properties of Certain Subclass of Multivalent Functions with Negative Coefficients

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Jingyu Yang ◽  
Shuhai Li
Keyword(s):  
Linear Operator ◽  
Fractional Calculus ◽  
Hadamard Product ◽  
Distortion Theorem ◽  
Coefficient Inequality ◽  
Radius Of Convexity ◽  
Convolution Properties

Making use of a linear operator, which is defined by the Hadamard product, we introduce and study a subclassYa,c+(A,B;p,λ,α)of the classA+(p). In this paper, we obtain the coefficient inequality, distortion theorem, radius of convexity and starlikeness, neighborhood property, modified convolution properties of this class. Furthermore, an application of fractional calculus operator is given. The results are presented here would provide extensions of some earlier works. Several new results are also obtained.

On some interesting properties for a new subclass of multivalent functions

2016 ◽  
Vol 09 (01) ◽  
pp. 1650027 ◽  
Author(s):  
M. Z. Ahmad ◽  
Rabha W. Ibrahim ◽  
Hiba F. Al-Janaby
Keyword(s):  
Linear Operator ◽  
Integral Representation ◽  
Distortion Theorem ◽  
Partial Sums ◽  
Closure Theorem ◽  
Radius Of Convexity

In this paper, we establish a new subfamily [Formula: see text] of multivalent functions with negative coefficients that involve certain linear operator. We first investigate sharp results concerning coefficients, then obtain the distortion theorem, radius of convexity and close-to-convexity, closure theorem, neighborhood property, partial sums and integral representation.

scholarly journals Certain Subclasses of Meromorphic Univalent Function Involving Differential Operator

2020 ◽  
Vol 31 (4) ◽  
pp. 80
Author(s):  
Teba Rzaij Al-Kubaisi ◽  
AbdulRahman Salman Juma
Keyword(s):  
Differential Operator ◽  
Univalent Function ◽  
Hadamard Product ◽  
Distortion Theorem ◽  
Geometric Properties ◽  
Growth Theorem ◽  
Coefficient Inequality

The main object of the present paper is to introduce the class of meromorphic univalent function K* (σ,τ,S) defined by differential operator with study some geometric properties like coefficient inequality , growth theorem and distortion theorem, radii of starlikeness and convexity of f(z) in the class K* (σ,τ,S) .Also the concept of convolution (Hadamard product) investigate and Neighborhoods of the elements of class K* (σ,τ,S) are obtained.

scholarly journals Some Geometric Properties for an Extended Class Involving Holomorphic Functions Defined by Fractional Calculus

2020 ◽  
pp. 1136-1145
Author(s):  
Sattar Kamil Hussein ◽  
Kassim Abdulhameed Jassim
Keyword(s):  
Fractional Calculus ◽  
Unit Disk ◽  
Fractional Derivatives ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Holomorphic Functions ◽  
Distortion Theorem ◽  
Fractional Integrals ◽  
Open Unit ◽  
Open Unit Disk

The main objective of" this paper is to study a subclass of holomrphic and univalent functions with negative coefficients in the open unit disk U= defined by Hadamard Product. We obtain coefficients estimates, distortion theorem , fractional derivatives, fractional integrals, and some results.

A subclass of meromorphic functions defined by a certain integral operator on Hilbert space

2017 ◽  
Vol 26 (2) ◽  
pp. 115-124
Author(s):  
Arzu Akgül
Keyword(s):  
Hilbert Space ◽  
Integral Operator ◽  
Meromorphic Functions ◽  
Hadamard Product ◽  
Extreme Points ◽  
Space Operator ◽  
Integral Means ◽  
New Class ◽  
Coefficient Inequality ◽  
Hilbert Space Operator

In the present paper, we introduce and investigate a new class of meromorphic functions associated with an integral operator, by using Hilbert space operator. For this class, we obtain coefficient inequality, extreme points, radius of close-to-convex, starlikeness and convexity, Hadamard product and integral means inequality.

scholarly journals A Subordination Principle on Wright Functions and Regularized Resolvent Families

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Luciano Abadias ◽  
Pedro J. Miana
Keyword(s):  
Fractional Calculus ◽  
Lévy Processes ◽  
Levy Processes ◽  
Laplace Transforms ◽  
Cauchy Problems ◽  
Convolution Properties ◽  
Vector Valued ◽  
Resolvent Families

We obtain a vector-valued subordination principle forgα,gβ-regularized resolvent families which unified and improves various previous results in the literature. As a consequence, we establish new relations between solutions of different fractional Cauchy problems. To do that, we consider scaled Wright functions which are related to Mittag-Leffler functions, the fractional calculus, and stable Lévy processes. We study some interesting properties of these functions such as subordination (in the sense of Bochner), convolution properties, and their Laplace transforms. Finally we present some examples where we apply these results.

Application of fractional calculus operators for a new class of univalent functions with negative coefficients defined by Hohlov operator

2010 ◽  
Vol 60 (1) ◽  
Author(s):  
Waggas Atshan
Keyword(s):  
Fractional Calculus ◽  
Unit Disc ◽  
Univalent Functions ◽  
Distortion Theorem ◽  
New Class ◽  
Fractional Calculus Operators ◽  
Coefficient Inequalities ◽  
Analytic And Univalent Functions

AbstractIn this paper, we introduce a new class W(a, b, c, γ, β) which consists of analytic and univalent functions with negative coefficients in the unit disc defined by Hohlov operator, we obtain distortion theorem using fractional calculus techniques for this class. Also coefficient inequalities and some results for this class are obtained.

scholarly journals Certain classes of univalent functions with negative coefficients II

1976 ◽  
Vol 15 (3) ◽  
pp. 467-473 ◽  
Author(s):  
V.P. Gupta ◽  
P.K. Jain
Keyword(s):  
Univalent Functions ◽  
Arithmetic Mean ◽  
Distortion Theorem ◽  
Linear Combinations ◽  
Radius Of Convexity ◽  
Image Position ◽  
Class Of Functions

Let P*(α, β) denote the class of functionsanalytic and univalent in |z| < 1 for whichwhere α є [0, 1), β є (0, 1].Sharp results concerning coefficients, distortion theorem and radius of convexity for the class P*(α, β) are determined. A comparable theorem for the classes C*(α, β) and P*(α, β) is also obtained. Furthermore, it is shown that the class P*(α, ß) is closed under ‘arithmetic mean’ and ‘convex linear combinations’.

scholarly journals Convolution properties for subclasses of meromorphic univalent functions of complex order

Filomat ◽  
2012 ◽  
Vol 26 (1) ◽  
pp. 153-163 ◽  
Author(s):  
Teodor Bulboacă ◽  
Mohamed Aouf ◽  
Rabha El-Ashwah
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Complex Order ◽  
Inclusion Relations ◽  
Coefficient Inequalities ◽  
Convolution Properties ◽  
Meromorphic Univalent Functions

Using the new linear operator Lm(?,l)f(z) = 1/z + ??k=1(l/l+ ?k)m akzk-1, f ? ?, where l > 0, ? ? 0, and m ? N0 = N ? {0}, we introduce two subclasses of meromorphic analytic functions, and we investigate several convolution properties, coefficient inequalities, and inclusion relations for these classes.

scholarly journals On Some new Results of a Subclass of Meromorphic Univalent Functions with Negative Coefficients Defined by liu – Srivastava Linear Operator

2018 ◽  
Vol 7 (4.36) ◽  
pp. 806
Author(s):  
Amal Mohammed Darweesh
Keyword(s):  
Linear Operator ◽  
Univalent Functions ◽  
Partial Sums ◽  
Closure Theorems ◽  
Distortion Theorems ◽  
Convolution Properties ◽  
Growth And Distortion Theorems ◽  
Meromorphic Univalent Functions

In this paper, we introduce and study a new subclass of meromorphic univalent functions with negative coefficients defined by Liu – Srivastava linear operator in the  We obtain some properties like, coefficients inequalities, growth and distortion theorems, closure theorems, partial sums and convolution properties.  

scholarly journals Subclass of p-valent Function with Negative Coefficients Applying Generalized Al-Oboudi Differential Operator

2021 ◽  
pp. 87-103
Author(s):  
Timilehin G. Shaba ◽  
Abd'gafar T. Tiamiyu ◽  
Ismaila O. Ibrahim ◽  
Abdullahi A. Ibrahim
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Distortion Theorem ◽  
Negative Coefficient ◽  
Growth Theorem ◽  
Coefficient Inequalities ◽  
Generalized Differential

In this paper we introduce a new subclass $\mathcal{R}^*(p,g,\psi,\varrho,\beta,\phi,\gamma,\zeta)$ of $p$-valent functions with negative coefficient defined by Hadamard product associated with a generalized differential operator. Radii of close-to-convexity, starlikeness and convexity of the class $\mathcal{R}^*(p,g,\psi,\varrho,\beta,\phi,\gamma,\zeta)$ are obtained. Also, distortion theorem, growth theorem and coefficient inequalities are established.

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