scholarly journals Neighborhoods of Certain Multivalently Analytic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Serap Bulut
Keyword(s):  
Analytic Functions ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Function Classes ◽  
Convolution Structure

We introduce and investigate two new general subclasses of multivalently analytic functions of complex order by making use of the familiar convolution structure of analytic functions. Among the various results obtained here for each of these function classes, we derive the coefficient bounds, distortion inequalities, and other interesting properties and characteristics for functions belonging to the classes introduced here.

scholarly journals Some New Inclusion and Neighborhood Properties for Certain Multivalent Function Classes Associated with the Convolution Structure

2008 ◽  
Vol 2008 ◽  
pp. 1-9
Author(s):  
J. K. Prajapat ◽  
R. K. Raina
Keyword(s):  
Analytic Functions ◽  
Multivalent Function ◽  
Complex Order ◽  
Function Classes ◽  
Convolution Structure

We use the familiar convolution structure of analytic functions to introduce two new subclasses of multivalently analytic functions of complex order, and prove several inclusion relationships associated with the -neighborhoods for these subclasses. Some interesting consequences of these results are also pointed out.

scholarly journals Inclusion and Neighborhood Properties for Certain Classes of Multivalently Analytic Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Serap Bulut
Keyword(s):  
Analytic Functions ◽  
Complex Order ◽  
Function Classes ◽  
Convolution Structure ◽  
Coefficient Inequalities

We introduce and investigate two new general subclasses of multivalently analytic functions of complex order by making use of the familiar convolution structure of analytic functions. Among the various results obtained here for each of these function classes, we derive the coefficient inequalities and other interesting properties and characteristics for functions belonging to the classes introduced here.

scholarly journals Geometric Properties of Certain Classes of Analytic Functions Associated with a q-Integral Operator

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 719 ◽  
Author(s):  
Shahid Mahmood ◽  
Nusrat Raza ◽  
Eman S. A. AbuJarad ◽  
Gautam Srivastava ◽  
H. M. Srivastava ◽  
...  
Keyword(s):  
Integral Operator ◽  
Bessel Function ◽  
Analytic Functions ◽  
Operator Coefficient ◽  
Geometric Properties ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Inclusion Relations

This article presents certain families of analytic functions regarding q-starlikeness and q-convexity of complex order γ ( γ ∈ C \ 0 ) . This introduced a q-integral operator and certain subclasses of the newly introduced classes are defined by using this q-integral operator. Coefficient bounds for these subclasses are obtained. Furthermore, the ( δ , q )-neighborhood of analytic functions are introduced and the inclusion relations between the ( δ , q )-neighborhood and these subclasses of analytic functions are established. Moreover, the generalized hyper-Bessel function is defined, and application of main results are discussed.

scholarly journals On subordination results for classes of analytic functions with a convolution structure

2010 ◽  
Vol 106 (2) ◽  
pp. 250
Author(s):  
J. K. Prajapat ◽  
R. K. Raina
Keyword(s):  
Analytic Functions ◽  
Function Classes ◽  
Convolution Structure ◽  
Differential Subordinations

By adapting a familiar convolution structure of analytic functions, we define and investigate in this paper certain new classes of analytic functions. Among the various results studied (by using the methods of differential subordinations) are some of the useful properties and characteristics attributed to these function classes. Several consequences of the main results are considered and relevant connections with some known results are also pointed out.

scholarly journals Certain Subclasses of Analytic Functions with Complex Order

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
A. Selvam ◽  
P. Sooriya Kala ◽  
N. Marikkannan
Keyword(s):  
Analytic Functions ◽  
Coefficient Bounds ◽  
Complex Order

Two new subclasses of analytic functions of complex order are introduced. Apart from establishing coefficient bounds for these classes, we establish inclusion relationships involving (n-δ) neighborhoods of analytic functions with negative coefficients belonging to these subclasses.

scholarly journals Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator

2021 ◽  
pp. 49-76
Author(s):  
Faroze Ahmad Malik ◽  
Nusrat Ahmed Dar ◽  
Chitaranjan Sharma
Keyword(s):  
Convex Functions ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Extreme Points ◽  
Integral Operators ◽  
Integral Means ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Special Cases ◽  
The Family

We use the concept of convolution to introduce and study the properties of a unified family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$, $(0\leq\gamma\leq1,\,k\geq0)$, consisting of uniformly $k$-starlike and $k$-convex functions of complex order $b\in\mathbb{C}\setminus\{0\}$ and type $\alpha\in[0,1)$. The family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$ is a generalization of several other families of analytic functions available in literature. Apart from discussing the coefficient bounds, sharp radii estimates, extreme points and the subordination theorem for this family, we settle down the Silverman's conjecture for integral means inequality. Moreover, invariance of this family under certain well-known integral operators is also established in this paper. Some previously known results are obtained as special cases.

scholarly journals Coefficient Bounds for Certain Subclasses of Analytic Functions Defined by Komatu Integral Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Serap Bulut
Keyword(s):  
Differential Equation ◽  
Integral Operator ◽  
Analytic Functions ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Type Differential Equation

We determine the coeffcient bounds for functions in certain subclasses of analytic functions of complex order, which are introduced here by means of a certain non-homogeneous Cauchy–Euler type differential equation of orderm. Relevant connections of some of the results obtained with those in earlier works are also provided.

On a certain class of analytic functions associated with a convolution structure

2008 ◽  
Vol 41 (3) ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
R. K. Raina
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Coefficient Bounds ◽  
New Class ◽  
Convolution Structure

AbstractMaking use of a convolution structure, we introduce a new class of analytic functions defined in the open unit disc and investigate its various characteristics. Apart from deriving a set of coefficient bounds, we establish several inclusion relationships involving the (

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