scholarly journals Certain Classes of Analytic Functions Bound with Kober Operators in q -Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
S. D. Purohit ◽  
M. M. Gour ◽  
S. Joshi ◽  
D. L. Suthar
Keyword(s):  
Analytic Functions ◽  
Open Disk ◽  
Coefficient Inequality ◽  
Analytical Functions ◽  
Distortion Theorems

Through applying the Kober fractional q -calculus apprehension, we preliminary implant and introduce new types of univalent analytical functions with a q -differintegral operator in the open disk U = ξ ∈ ℂ : ∣ ξ | < 1 . The coefficient inequality and distortion theorems are among the results examined with these forms of functions. Specific cases are responded and addressed immediately. The findings include an expansion of the numerous established results in the q -theory of analytical functions.

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.

scholarly journals A coefficient inequality for the class of analytic functions in the unit disc

2003 ◽  
Vol 2003 (59) ◽  
pp. 3753-3759
Author(s):  
Yaşar Polatoğlu ◽  
Metın Bolcal
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Coefficient Inequality

The aim of this paper is to give a coefficient inequality for the class of analytic functions in the unit discD={z||z| <1}.

scholarly journals Some Properties of Subclasses of Multivalent Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Muhammet Kamali ◽  
Fatma Sağsöz
Keyword(s):  
Analytic Functions ◽  
Partial Sums ◽  
Coefficient Inequality

The authors introduce two new subclasses denoted by and of the class of -valent analytic functions. They obtain coefficient inequality for the class . They investigate various properties of classes and . Furthermore, they derive partial sums associated with the class .

Distortion theorems in the class Kn(D)

2008 ◽  
Vol 41 (3) ◽  
Author(s):  
Eduard G. Kir’yatskii
Keyword(s):  
Analytical Functions ◽  
Distortion Theorems

AbstractThis article presents the analysis of properties of functions belonging to the class KThe subclass K̃The author touches classical and at the same time urgent questions, arising at the study of analytical functions, belonging to some class.

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.

ON CERTAIN SUBCLASS OF p-VALENT NON-BAZILEVIC FUNCTIONS DEFINED BY THE DZIOK–SRIVASTAVA OPERATOR

2013 ◽  
Vol 06 (03) ◽  
pp. 1350032
Author(s):  
T. M. Seoudy ◽  
M. K. Aouf
Keyword(s):  
Analytic Functions ◽  
Principle Of Subordination ◽  
Distortion Theorems ◽  
Convolution Properties ◽  
Bazilevic Functions

By making use of the principle of subordination and Dziok–Srivastava operator, we introduce a certain subclass of p-valent non-Bazilevic analytic functions. Such results as subordination and superordination properties, convolution properties, distortion theorems and inequality properties, are proved.

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