COEFFICIENT INEQUALITIES FOR A CLASS OF p-VALENT ANALYTIC FUNCTIONS DEFINED BY USING FRACTIONAL CALCULUS OPERATORS

2015 ◽  
Vol 96 (4) ◽  
pp. 463-474
Author(s):  
K. A. Selvakumaran ◽  
Geetha Balachandar ◽  
P. Rajaguru
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
Fractional Calculus Operators ◽  
Coefficient Inequalities

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 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.

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