Integral means of certain analytic functions for fractional calculus

2007 ◽  
Vol 187 (1) ◽  
pp. 425-432 ◽  
Author(s):  
Tadayuki Sekine ◽  
Shigeyoshi Owa ◽  
Kazuyuki Tsurumi
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
Integral Means

Some properties for certain subclasses of analytic functions defined by a general differential operator

2019 ◽  
Vol 13 (07) ◽  
pp. 2050134
Author(s):  
Erhan Deniz ◽  
Murat Çağlar ◽  
Yücel Özkan
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Partial Sums ◽  
Integral Means

In this paper, we study two new subclasses [Formula: see text] and [Formula: see text] of analytic functions which are defined by means of a differential operator. Some results connected to partial sums and neighborhoods and integral means related to these subclasses are obtained.

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.

THE INCREMENTAL RATIO BASED CAUSAL FRACTIONAL CALCULUS

2012 ◽  
Vol 22 (04) ◽  
pp. 1250078 ◽  
Author(s):  
MANUEL D. ORTIGUEIRA ◽  
MARGARITA RIVERO ◽  
JUAN J. TRUJILLO
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Analytic Functions ◽  
Group Structure ◽  
Semi Group ◽  
Set Up

The generalized incremental ratio fractional derivative is revised and its main properties deduced. It is shown that in the case of analytic functions, it enjoys some interesting properties like: linearity and causality and has a semi-group structure. Some simple examples are presented. The enlargement of the set of functions for which the group properties of the fractional derivative are valid is done. With this, it is shown that some well-known results are valid in a more general set-up. Some examples are presented.

scholarly journals A New Class of Analytic Functions Defined by Using Salagean Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
R. M. El-Ashwah ◽  
M. K. Aouf ◽  
A. A. M. Hassan ◽  
A. H. Hassan
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Integral Means ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Fractional Calculus Operators

We derive some results for a new class of analytic functions defined by using Salagean operator. We give some properties of functions in this class and obtain numerous sharp results including for example, coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, integral means inequalities, and partial sums of functions belonging to this class. Finally, we give an application involving certain fractional calculus operators that are also considered.

scholarly journals Integral means of certain class of analytic functions

1993 ◽  
Vol 16 (3) ◽  
pp. 459-464
Author(s):  
Gao Chunyi
Keyword(s):  
Analytic Functions ◽  
Starlike Function ◽  
Integral Means ◽  
Alpha Beta ◽  
Class Of Functions ◽  
Extremal Properties

In this paper we discuss the following class of functionsSλ(α,β)={f(z):|f(z)g(z)−1|<β|λf(z)g(z)+1|,z∈D}  where  0≤λ≤1,0<β≤1,0≤α<1, andf(z)=z+∑n=2∞anznis analytic inD={z:|z|<1},g(z)is a starlike function of orderα. A subordination about this class is obtained, the integral means of functions inSλ(α,β)and some extremal properties are studied.

scholarly journals A subordination results for a class of analytic functions defined by q-differential operator

2020 ◽  
Vol 19 (1) ◽  
pp. 53-64 ◽  
Author(s):  
Basem Aref Frasin ◽  
Gangadharan Murugusundaramoorthy
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Integral Means

AbstractIn this paper, we derive several subordination results and integral means result for certain class of analytic functions defined by means of q-differential operator. Some interesting corollaries and consequences of our results are also considered.

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