scholarly journals On new classes of analytic functions with negative coefficients

1984 ◽  
Vol 7 (4) ◽  
pp. 719-730 ◽  
Author(s):  
Shigeyoshi Owa
Keyword(s):  
Analytic Functions ◽  
Hadamard Product ◽  
Ruscheweyh Derivative ◽  
Closure Theorems ◽  
Coefficient Inequalities

We introduce the classesKn*of analytic functions with negative coefficients by using thenth order Ruscheweyh derivative. The object of the present paper is to show coefficient inequalities and some closure theorems for functionsf(z)inKn*. Further we consider the modified Hadamard product of functionsfi(z)inKni*(n=1,2,…,m).

Results of differential subordination for a unified subclass of analytic functions defined using generalized Ruscheweyh derivative operator

2019 ◽  
Vol 12 (03) ◽  
pp. 1950035
Author(s):  
Ritu Agarwal ◽  
G. S. Paliwal ◽  
Parany Goswami
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Sandwich Theorem ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Principle Of Subordination ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In this paper, we introduce a unified subclass of analytic functions by making use of the principle of subordination, involving generalized Ruscheweyh Derivative operator [Formula: see text]. The properties such as inclusion relationships, distortion theorems, coefficient inequalities and differential sandwich theorem for the above class have been discussed.

scholarly journals Applications of a Multiplier Transformation and Ruscheweyh Derivative for Obtaining New Strong Differential Subordinations

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1312
Author(s):  
Alina Alb Lupaş
Keyword(s):  
Analytic Functions ◽  
Hadamard Product ◽  
Ruscheweyh Derivative ◽  
Differential Subordinations ◽  
Multiplier Transformation

Here, we study strong differential subordinations for the extended new operator IRλ,lm defined by the Hadamard product of the extended multiplier transformation Im,λ,l and the extended Ruscheweyh derivative Rm, on the class of normalized analytic functions Anζ∗={f∈H(U×U¯),f(z,ζ)=z+an+1ζzn+1+⋯,z∈U,ζ∈U¯}, by IRλ,lm:Anζ∗→Anζ∗, IRλ,lmfz,ζ=Im,λ,l∗Rmfz,ζ.

scholarly journals Fekete-Szegö Type Coefficient Inequalities for Certain Subclass of Analytic Functions and Their Applications Involving the Owa-Srivastava Fractional Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Serap Bulut
Keyword(s):  
Analytic Functions ◽  
Hadamard Product ◽  
Type Inequality ◽  
Fractional Operator ◽  
Special Cases ◽  
Coefficient Inequalities

A new subclass of analytic functions is introduced. For this class, firstly the Fekete-Szegö type coefficient inequalities are derived. Various known or new special cases of our results are also pointed out. Secondly some applications of our main results involving the Owa-Srivastava fractional operator are considered. Thus, as one of these applications of our result, we obtain the Fekete-Szegö type inequality for a class of normalized analytic functions, which is defined here by means of the Hadamard product (or convolution) and the Owa-Srivastava fractional operator.

scholarly journals On Subclass of Analytic Univalent Functions Associated with Negative Coefficients

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Ma'moun Harayzeh Al-Abbadi ◽  
Maslina Darus
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Derivative Operator ◽  
Generalized Derivative ◽  
Closure Theorems ◽  
Coefficient Inequalities ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

M. H. Al-Abbadi and M. Darus (2009) recently introduced a new generalized derivative operatorμλ1,λ2n,m, which generalized many well-known operators studied earlier by many different authors. In this present paper, we shall investigate a new subclass of analytic functions in the open unit diskU={z∈ℂ:|z|<1}which is defined by new generalized derivative operator. Some results on coefficient inequalities, growth and distortion theorems, closure theorems, and extreme points of analytic functions belonging to the subclass are obtained.

scholarly journals A New Subclass ofk-Janowski Type Functions Associated with Ruscheweyh Derivative

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Shahid Mahmood ◽  
Sarfraz Nawaz Malik ◽  
Saima Mustafa ◽  
S. M. Jawwad Riaz
Keyword(s):  
Analytic Functions ◽  
General Class ◽  
Integral Transform ◽  
Ruscheweyh Derivative ◽  
Coefficient Inequalities

We introduce and investigate a new subclassVDkA,B,b,δof analytic functions using Ruscheweyh derivative. We derive the coefficient inequalities and other interesting properties and characteristics for functions belonging to the general class, which we have introduced and studied in this article. We also observe that this class is preserved under the Bernardi integral transform.

scholarly journals A GENERALIZATION OF CERTAIN CLASS OF ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS

1995 ◽  
Vol 26 (2) ◽  
pp. 107-117
Author(s):  
M. K. AOUF ◽  
A. SHAMANDY
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Fractional Operators ◽  
Coefficient Estimates ◽  
Func Tions ◽  
Closure Theorems ◽  
Distortion Theorems ◽  
Radius Of Univalence

We introduce the subclass $T^*(A,B,n,a)$ ($-1 \le A < B\le 1$, $0 < B \le 1$, $n \ge 0$, and $0\le\alpha <1$) of analytic func;tions with negative coefficients by the operator $D^n$. Coefficient estimates, distortion theorems, closure theorems and radii of close-to-convexety, starlikeness and convexity for the class $T^*(A,B,n,a)$ are determined. We also prove results involving the modified Hadamard product of two functions associated with the class $T^*(A,B,n,a)$. Also we obtain Several interesting distortion theorems for certain fractional operators .of functions in the class $T^*(A,B,n,a)$. Also we obtain class perserving integral operator of the form \[F(z)=\afrc{c+1}{z^c}\int_0^z t^{c-1}f(t) dt, \quad c>-1\] for the class $T^*(A,B,n,a)$. Conversely when $F(z) \in T*(A,B,n,a)$, radius of univalence of $f(z)$ defined by the above equation is obtained.

scholarly journals Modified Hadamard product properties of certain class of analytic functions with varying arguments defined by the convolution of Sǎlǎgean and Ruscheweyh derivative

2019 ◽  
Vol 11 (2) ◽  
pp. 350-362
Author(s):  
Ágnes Orsolya Páll-Szabó
Keyword(s):  
Analytic Functions ◽  
Hadamard Product ◽  
Ruscheweyh Derivative ◽  
Varying Arguments

Abstract In this paper we study the Hadamard product properties of certain class of analytic functions with varying arguments defined by the convolution of Sǎlǎgean and Ruscheweyh derivative. The obtained results are sharp and they improve known results.

scholarly journals Properties on a subclass of univalent functions defined by using a multiplier transformation and Ruscheweyh derivative

2015 ◽  
Vol 23 (1) ◽  
pp. 9-24
Author(s):  
Alina Alb Lupaş
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Coefficient Estimates ◽  
Ruscheweyh Derivative ◽  
Closure Theorems ◽  
Distortion Theorems ◽  
Multiplier Transformation

AbstractIn this paper we have introduced and studied the subclass ℛ𝒥 (d, α, β) of univalent functions defined by the linear operator $RI_{n,\lambda ,l}^\gamma f(z)$ defined by using the Ruscheweyh derivative Rnf(z) and multiplier transformation I (n, λ, l) f(z), as $RI_{n,\lambda ,l}^\gamma :{\cal A} \to {\cal A}$, $RI_{n,\lambda ,l}^\gamma f(z) = (1 - \gamma )R^n f(z) + \gamma I(n,\lambda ,l)f(z)$, z ∈ U, where 𝒜n ={f ∈ ℋ(U) : f(z) = z + an+1zn+1 + . . . , z ∈ U}is the class of normalized analytic functions with 𝒜1 = 𝒜. The main object is to investigate several properties such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity and close-to-convexity of functions belonging to the class ℛ𝒥(d, α, β).

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