scholarly journals Certain Class of Analytic Functions with respect to Symmetric Points Defined by Q-Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
K. R. Karthikeyan ◽  
G. Murugusundaramoorthy ◽  
S. D. Purohit ◽  
D. L. Suthar
Keyword(s):  
Integral Representation ◽  
Representation Theorem ◽  
Analytic Functions ◽  
Type Star ◽  
Coefficient Bounds ◽  
Quantum Calculus ◽  
Complex Order ◽  
Special Cases ◽  
Symmetric Points

In this study, we familiarise a novel class of Janowski-type star-like functions of complex order with regard to j , k -symmetric points based on quantum calculus by subordinating with pedal-shaped regions. We found integral representation theorem and conditions for starlikeness. Furthermore, with regard to j , k -symmetric points, we successfully obtained the coefficient bounds for functions in the newly specified class. We also quantified few applications as special cases which are new (or known).

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 Multivalent Prestarlike Functions with Respect to Symmetric Points

Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 20
Author(s):  
Daniel Breaz ◽  
Kadhavoor R. Karthikeyan ◽  
Alagiriswamy Senguttuvan
Keyword(s):  
Integral Representation ◽  
Function Class ◽  
Coefficient Estimates ◽  
Quantum Calculus ◽  
Complex Order ◽  
Inclusion Relations ◽  
Symmetric Points

A class of p-valent functions of complex order is defined with the primary motive of unifying the concept of prestarlike functions with various other classes of multivalent functions. Interesting properties such as inclusion relations, integral representation, coefficient estimates and the solution to the Fekete–Szegő problem are obtained for the defined function class. Further, we extended the results using quantum calculus. Several consequences of our main results are pointed out.

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 the generalised Ruscheweyh class of analytic functions of complex order

1993 ◽  
Vol 47 (2) ◽  
pp. 247-257 ◽  
Author(s):  
O.P. Ahuja
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Order Complex ◽  
Sharp Estimates ◽  
Complex Order ◽  
Special Cases ◽  
The Family ◽  
Uniform Treatment

The main object of this paper is to identify various classes of analytic functions which are starlike, convex, pre-starlike, Ruscheweyh class of order α, β-spiral-like, β-convex-spiral-like, starlike of complex order, complex of complex order, and others as special cases of a family of analytic functions of complex order in the unit disk. This makes a uniform treatment possible. Finally, we derive sharp estimates for all coefficients of the functions from the family.

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.

A generalized class of α-convex functions with respect to n-symmetric points

2021 ◽  
pp. 2250099
Author(s):  
A. Y. Lashin ◽  
F. Z. El-Emam
Keyword(s):  
Integral Representation ◽  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Symmetric Points

In this paper, we investigate certain subclass of analytic functions on the open unit disc. This class generalizes the well-known class of [Formula: see text]-convex functions with respect to n-symmetric points. Some interesting properties such as subordination results, containment relations, integral preserving properties, and the integral representation for functions in this class are obtained.

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 q–analogue of generalized Ruschweyh operator related to a new subfamily of multivalent functions

2019 ◽  
Vol 27 (2) ◽  
pp. 59-69
Author(s):  
Shahram Najafzadeh ◽  
Mugur Acu
Keyword(s):  
Integral Representation ◽  
Analytic Functions ◽  
Integral Operators ◽  
Arithmetic Mean ◽  
Coefficient Bounds

AbstractA new subfamily of p–valent analytic functions with negative coefficients in terms of q–analogue of generalized Ruschweyh operator is considered. Several properties concerning coefficient bounds, weighted and arithmetic mean, radii of starlikeness, convexity and close-to-convexity are obtained. A family of class preserving integral operators and integral representation are also indicated.

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.

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