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 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 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 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.

New Classification of Gemstone Colours

1971 ◽  
Vol 12 (7) ◽  
pp. 262-266
Author(s):  
K. F. Chudoba
Keyword(s):  
New Classification

Reductionism and holism in the philosophy of medicine

2020 ◽  
pp. 66-74
Author(s):  
E. Zakablukovskiy
Keyword(s):  
Philosophy Of Medicine ◽  
Point Of View ◽  
Social Model ◽  
Macro Level ◽  
New Classification

The article highlights certain aspects of the discussion on the topic of reductionism vs. holism in the philosophy of medicine. Classic radical reductionism is defeated by the concept of emergence. The s.c. bio-medical point of view on a malady, despite its relevance and clear benefit, is not recognized as universal as its adherents may claim, and it yields to an integral psycho-bio-social model. The author introduces a new classification of holism (vitalistic, social and individualistic) and makes appropriate recommendations to clinicians. It is social holism at the macro level that has proven effective in combating the spread of COVID-19.

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