scholarly journals A Subclass of Multivalent Janowski Type q-Starlike Functions and Its Consequences

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1275
Author(s):  
Qiuxia Hu ◽  
Hari M. Srivastava ◽  
Bakhtiar Ahmad ◽  
Nazar Khan ◽  
Muhammad Ghaffar Khan ◽  
...  
Keyword(s):  
Analytic Functions ◽  
Convex Combination ◽  
Starlike Functions ◽  
Function Class ◽  
Additional Parameter ◽  
Growth Theorem ◽  
Function Classes ◽  
Geometric Function ◽  
Janowski Functions ◽  
Principle Of Subordination

In this article, by utilizing the theory of quantum (or q-) calculus, we define a new subclass of analytic and multivalent (or p-valent) functions class Ap, where class Ap is invariant (or symmetric) under rotations. The well-known class of Janowski functions are used with the help of the principle of subordination between analytic functions in order to define this subclass of analytic and p-valent functions. This function class generalizes various other subclasses of analytic functions, not only in classical Geometric Function Theory setting, but also some q-analogue of analytic multivalent function classes. We study and investigate some interesting properties such as sufficiency criteria, coefficient bounds, distortion problem, growth theorem, radii of starlikeness and convexity for this newly-defined class. Other properties such as those involving convex combination are also discussed for these functions. In the concluding part of the article, we have finally given the well-demonstrated fact that the results presented in this article can be obtained for the (p,q)-variations, by making some straightforward simplification and will be an inconsequential exercise simply because the additional parameter p is obviously unnecessary.

scholarly journals A Subclass of Janowski Starlike Functions Involving Mathieu-Type Series

Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 2
Author(s):  
Dong Liu ◽  
Serkan Araci ◽  
Bilal Khan
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Function Class ◽  
Partial Sums ◽  
Invariant Functions ◽  
Type Series ◽  
Janowski Functions ◽  
Radius Problems ◽  
Symmetrical Points

To date, many interesting subclasses of analytic functions involving symmetrical points and other well celebrated domains have been investigated and studied. The aim of our present investigation is to make use of certain Janowski functions and a Mathieu-type series to define a new subclass of analytic (or invariant) functions. Our defined function class is symmetric under rotation. Some useful results like Fekete-Szegö functional, a number of sufficient conditions, radius problems, and results related to partial sums are derived.

scholarly journals Applications of Certain Conic Domains to a Subclass of q-Starlike Functions Associated with the Janowski Functions

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 574
Author(s):  
Bilal Khan ◽  
Hari Mohan Srivastava ◽  
Nazar Khan ◽  
Maslina Darus ◽  
Qazi Zahoor Ahmad ◽  
...  
Keyword(s):  
Lower Bounds ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Function Class ◽  
Partial Sums ◽  
Open Unit ◽  
Additional Parameter ◽  
Open Unit Disk ◽  
Janowski Functions ◽  
Distortion Theorems

In our present investigation, with the help of the basic (or q-) calculus, we first define a new domain which involves the Janowski function. We also define a new subclass of the class of q-starlike functions, which maps the open unit disk U, given by U= z:z∈C and z <1, onto this generalized conic type domain. We study here some such potentially useful results as, for example, the sufficient conditions, closure results, the Fekete-Szegö type inequalities and distortion theorems. We also obtain the lower bounds for the ratio of some functions which belong to this newly-defined function class and for the sequences of the partial sums. Our results are shown to be connected with several earlier works related to the field of our present investigation. Finally, in the concluding section, we have chosen to reiterate the well-demonstrated fact that any attempt to produce the rather straightforward (p,q)-variations of the results, which we have presented in this article, will be a rather trivial and inconsequential exercise, simply because the additional parameter p is obviously redundant.

scholarly journals On Janowski Analytic p,q-Starlike Functions in Symmetric Circular Domain

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Basem Aref Frasin ◽  
Thabet Abdeljawad
Keyword(s):  
Analytic Functions ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Circular Domain ◽  
Arithmetic Mean ◽  
Necessary And Sufficient Conditions ◽  
Weighted Mean ◽  
Growth Theorem ◽  
Necessary And Sufficient

The main object of the present paper is to apply the concepts of p,q-derivative by establishing a new subclass of analytic functions connected with symmetric circular domain. Further, we investigate necessary and sufficient conditions for functions belonging to this class. Convex combination, weighted mean, arithmetic mean, growth theorem, and convolution property are also determined.

scholarly journals Certain subclass of analytic functions with respect to symmetric points associated with conic region

2021 ◽  
Vol 6 (11) ◽  
pp. 12863-12877
Author(s):  
Huo Tang ◽  
◽  
Kadhavoor Ragavan Karthikeyan ◽  
Gangadharan Murugusundaramoorthy ◽  
◽  
...  
Keyword(s):  
Analytic Functions ◽  
Function Class ◽  
Quantum Calculus ◽  
Function Classes ◽  
Janowski Functions ◽  
Symmetric Points ◽  
Inverse Functions ◽  
Ordinary Derivative

<abstract><p>The purpose of this paper is to introduce and study a new subclass of analytic functions with respect to symmetric points associated to a conic region impacted by Janowski functions. Also, the study has been extended to quantum calculus by replacing the ordinary derivative with a $ q $-derivative in the defined function class. Interesting results such as initial coefficients of inverse functions and Fekete-Szegö inequalities are obtained for the defined function classes. Several applications, known or new of the main results are also presented.</p></abstract>

scholarly journals On a class of analytic functions related to Robertson’s formula and subordination

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Adam Lecko ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Integral Representation ◽  
Analytic Functions ◽  
Boundary Point ◽  
Unit Disc ◽  
Starlike Functions ◽  
Analytic Formula ◽  
Growth Theorem

AbstractIn this paper, we define and study a class of analytic functions in the unit disc by modification of the well-known Robertson’s analytic formula for starlike functions with respect to a boundary point combined with subordination. An integral representation and growth theorem are proved. Early coefficients and the Fekete–Szegö functional are also estimated.

Some properties of the analytic functions with bounded radius rotation

2019 ◽  
Vol 28 (1) ◽  
pp. 85-90
Author(s):  
YASAR POLATOGLU ◽  
◽  
ASENA CETINKAYA ◽  
OYA MERT ◽  
◽  
...  
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Coefficient Estimate ◽  
Open Unit Disc ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
Bounded Radius Rotation

In the present paper, we introduce a new subclass of normalized analytic starlike functions by using bounded radius rotation associated with q- analogues in the open unit disc \mathbb D. We investigate growth theorem, radius of starlikeness and coefficient estimate for the new subclass of starlike functions by using bounded radius rotation associated with q- analogues denoted by \mathcal{R}_k(q), where k\geq2, q\in(0,1).

scholarly journals EXTREME POINTS OF INTEGRAL FAMILIES OF ANALYTIC FUNCTIONS

2013 ◽  
Vol 94 (2) ◽  
pp. 202-221
Author(s):  
KEIKO DOW ◽  
D. R. WILKEN
Keyword(s):  
Analytic Functions ◽  
Compact Convex ◽  
Extreme Points ◽  
Starlike Functions ◽  
Extremal Problems ◽  
Kernel Functions ◽  
Closed Convex Hull ◽  
New Class ◽  
Geometric Function ◽  
Derivatives Of

AbstractExtreme points of compact, convex integral families of analytic functions are investigated. Knowledge about extreme points provides a valuable tool in the optimization of linear extremal problems. The functions studied are determined by a two-parameter collection of kernel functions integrated against measures on the torus. For specific choices of the parameters many families from classical geometric function theory are included. These families include the closed convex hull of the derivatives of normalized close-to-convex functions, the ratio of starlike functions of different orders, as well as many others. The main result introduces a surprising new class of extreme points.

scholarly journals Higher-order q-derivatives and their applications to subclasses of multivalent Janowski type q-starlike functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bilal Khan ◽  
Zhi-Guo Liu ◽  
H. M. Srivastava ◽  
Serkan Araci ◽  
Nazar Khan ◽  
...  
Keyword(s):  
Starlike Functions ◽  
Higher Order ◽  
Sufficient Condition ◽  
Function Classes ◽  
Janowski Functions ◽  
Radius Problems ◽  
Coefficient Inequalities

AbstractIn the present investigation, with the help of certain higher-order q-derivatives, some new subclasses of multivalent q-starlike functions which are associated with the Janowski functions are defined. Then, certain interesting results, for example, radius problems and the results related to distortion, are derived. We also derive a sufficient condition and certain coefficient inequalities for our defined function classes. Some known consequences related to this subject are also highlighted. Finally, the well-demonstrated fact about the $(p,q)$ ( p , q ) -variations is also given in the concluding section.

scholarly journals Applications of Mittag-Leffer Type Poisson Distribution to a Subclass of Analytic Functions Involving Conic-Type Regions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Nazar Khan ◽  
Wali Khan Mashwani ◽  
Sama Arjika ◽  
...  
Keyword(s):  
Poisson Distribution ◽  
Analytic Functions ◽  
Convex Combination ◽  
Partial Sums ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Geometric Properties ◽  
Distortion Bounds ◽  
Janowski Functions ◽  
Necessary And Sufficient

In this article, we introduce a new subclass of analytic functions utilizing the idea of Mittag-Leffler type Poisson distribution associated with the Janowski functions. Further, we discuss some important geometric properties like necessary and sufficient condition, convex combination, growth and distortion bounds, Fekete-Szegö inequality, and partial sums for this newly defined class.

scholarly journals On starlike functions associated with cardioid domain

2021 ◽  
Vol 109 (123) ◽  
pp. 95-107
Author(s):  
Saira Zainab ◽  
Mohsan Raza ◽  
Janusz Sokół ◽  
Sarfraz Malik
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Function Theory ◽  
Starlike Functions ◽  
Geometric Function Theory ◽  
Geometrical Structures ◽  
Image Domain ◽  
Geometric Function ◽  
Comprehensive Study

Analytic functions are characterized by the geometry of their image domains. That?s why, geometry of image domain is of substantial importance to have a comprehensive study of analytic functions. To introduce and study new geometrical structures as image domain and to define their subsequent analytic functions is an ongoing part of research in geometric function theory. We introduced a new domain named as cardioid domain and defined the corresponding analytic function, see [14]. Here we further study the cardioid domain, to define and study starlike functions associated with cardioid domain.

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