scholarly journals Generalization of certain subclasses of analytic functions

1987 ◽  
Vol 10 (4) ◽  
pp. 725-732 ◽  
Author(s):  
Tadayuki Sekine
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
Coefficient Inequalities ◽  
Distortion Theorems

We introduce the subclassTj(n,m,α)of analytic functions with negative coefficients by the operatorDn. Coefficient inequalities and distortion theorems of functions inTj(n,m,α)are determind. Further, distortion theorems for fractional calculus of functions inTj(n,m,α)are obtained.

scholarly journals Certain subclasses of analytic functions associated with fractional $q$-calculus operators

2011 ◽  
Vol 109 (1) ◽  
pp. 55 ◽  
Author(s):  
Sunil Dutt Purohit ◽  
Ravinder Krishna Raina
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
Open Disk ◽  
Q Theory ◽  
Special Cases ◽  
Coefficient Inequalities ◽  
Distortion Theorems

We first define the $q$-analogue operators of fractional calculus which are then used in defining certain classes of functions analytic in the open disk. The results investigated for these classes of functions include the coefficient inequalities and some distortion theorems. The results provide extensions of various known results in the $q$-theory of analytic functions. Special cases of our results are pointed out briefly.

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 New classification of analytic functions with negative coefficients

1988 ◽  
Vol 11 (1) ◽  
pp. 55-69
Author(s):  
Shigeyoshi Owa ◽  
Milutin Obradovic
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
Negative Coefficient ◽  
New Classification ◽  
Distortion Theorems

New classification of analytic functions with negative coefficients is given by using the coefficients inequality, that is, new subclassA(p,n,Bk)of analytic functions with negative coefficient is defined. The object of the present paper is to prove various distortion theorems for functions inA(p,n,Bk), and for fractional calculus of functions belonging toA(p,n,Bk). Further, some properties of the classA(p,n,Bk)are shown.

scholarly journals Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions

1987 ◽  
Vol 106 ◽  
pp. 1-28 ◽  
Author(s):  
H. M. Srivastava ◽  
Shigeyoshi Owa
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Linear Operators ◽  
Coefficient Estimates ◽  
Hadamard Products ◽  
Generalized Hypergeometric Functions ◽  
Hypergeometric Type ◽  
Distortion Theorems ◽  
Characterization Theorems

By using a certain linear operator defined by a Hadamard product or convolution, several interesting subclasses of analytic functions in the unit disk are introduced and studied systematically. The various results presented here include, for example, a number of coefficient estimates and distortion theorems for functions belonging to these subclasses, some interesting relationships between these subclasses, and a wide variety of characterization theorems involving a certain functional, some general functions of hypergeometric type, and operators of fractional calculus. Some of the coefficient estimates obtained here are fruitfully applied in the investigation of certain subclasses of analytic functions with fixed finitely many coefficients.

scholarly journals Certain Subclasses of Multivalent Functions Defined by Higher-Order Derivative

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Xiaofei Li ◽  
Deng Ding ◽  
Liping Xu ◽  
Chuan Qin ◽  
Songbo Hu
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Higher Order ◽  
Order Derivative ◽  
Special Cases ◽  
Higher Order Derivative ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In this paper, we define and study some subclasses of multivalent analytic functions of higher order in the unit disc. These classes generalize some classes previously studied. We obtain coefficient inequalities, distortion theorems, extreme points, and integral mean inequalities. We derive some results as special cases.

scholarly journals Applications of fractional calculus to $ k $-uniformly starlike and $ k $-uniformly convex functions of order $ \alpha $

2007 ◽  
Vol 38 (2) ◽  
pp. 103-109 ◽  
Author(s):  
Ajab Akbarally ◽  
Maslina Darus
Keyword(s):  
Fractional Calculus ◽  
Convex Functions ◽  
Analytic Functions ◽  
Uniformly Convex ◽  
Coefficient Bounds ◽  
Uniformly Convex Functions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems ◽  
Uniformly Starlike

A new subclass of analytic functions $ k-SP_\lambda(\alpha) $ is introduced by applying certain operators of fractional calculus to $k$-uniformly starlike and $ k $-uniformly convex functions of order $ \alpha $. Some theorems on coefficient bounds and growth and distortion theorems for this subclass are found. The radii of close to convexity, starlikeness and convexity for this subclass is also derived.

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 Properties of a New Subclass of Analytic Functions With Negative Coefficients Defined by Using the Q-Derivative

2020 ◽  
Vol 5 (1) ◽  
pp. 303-308
Author(s):  
Roberta Bucur ◽  
Daniel Breaz
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
New Class ◽  
Coefficient Inequalities ◽  
Distortion Theorems

AbstractIn this paper we define a new class of analytic functions with negative coefficients involving the q-differential operator. Our main purpose is to determine coefficient inequalities and distortion theorems for functions belonging to this class. Connections with previous results are pointed out.

scholarly journals Comprehensive family of uniformly analytic functions

2005 ◽  
Vol 36 (3) ◽  
pp. 243-254 ◽  
Author(s):  
B. A. Frasin
Keyword(s):  
Analytic Functions ◽  
Integral Operators ◽  
Hadamard Products ◽  
Closure Theorems ◽  
Coefficient Inequalities ◽  
Alpha Beta ◽  
Distortion Theorems

We introduce the subclass $ \mathcal{U}_{\mathcal{T}}(\Phi ,\Psi ;\alpha ,\beta ) $ of analytic functions with negative coefficients. Coefficient inequalities, distortion theorems, closure theorems, radii of close-to-convexity, starlikeness, and convexity for functions belonging to the class $ \mathcal{U}_{\mathcal{T}}(\Phi ,\Psi ;\alpha ,\beta ) $ are obtained. We also determine integral operators for functions in this class and some properties involving modified Hadamard products of several functions belonging to the class $ \mathcal{U}_{\mathcal{T}}^*(\Phi ,\Psi ;\alpha ,\beta ) $.

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