Applications of higher-order q-derivatives to the subclass of q-starlike functions associated with the Janowski functions

2021 ◽  
Vol 6 (2) ◽  
pp. 1110-1125
Author(s):  
Muhammad Sabil Ur Rehman ◽  
◽  
Qazi Zahoor Ahmad ◽  
H. M. Srivastava ◽  
Nazar Khan ◽  
...  
Keyword(s):  
Starlike Functions ◽  
Higher Order ◽  
Janowski Functions

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 Some Coefficient Inequalities of q-Starlike Functions Associated with Conic Domain Defined by q-Derivative

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Shahid Mahmood ◽  
Mehwish Jabeen ◽  
Sarfraz Nawaz Malik ◽  
H. M. Srivastava ◽  
Rabbiya Manzoor ◽  
...  
Keyword(s):  
Starlike Functions ◽  
Conic Domain ◽  
Janowski Functions ◽  
Coefficient Inequalities

This article deals with q-starlike functions associated with conic domains, defined by Janowski functions. It generalizes the recent study of q-starlike functions while associating it with the conic domains. Certain renowned coefficient inequalities in connection with the previously known ones have been included in this work.

scholarly journals Some General Classes of q-Starlike Functions Associated with the Janowski Functions

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 292 ◽  
Author(s):  
Hari Srivastava ◽  
Muhammad Tahir ◽  
Bilal Khan ◽  
Qazi Ahmad ◽  
Nazar Khan
Keyword(s):  
Unit Disk ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Janowski Functions ◽  
Distortion Theorems ◽  
The Relationship

By making use of the concept of basic (or q-) calculus, various families of q-extensions of starlike functions of order α in the open unit disk U were introduced and studied from many different viewpoints and perspectives. In this paper, we first investigate the relationship between various known classes of q-starlike functions that are associated with the Janowski functions. We then introduce and study a new subclass of q-starlike functions that involves the Janowski functions. We also derive several properties of such families of q-starlike functions with negative coefficients including (for example) distortion theorems.

Sharp coefficient bounds for starlike functions associated with the Bell numbers

2019 ◽  
Vol 69 (5) ◽  
pp. 1053-1064 ◽  
Author(s):  
Virendra Kumar ◽  
Nak Eun Cho ◽  
V. Ravichandran ◽  
H. M. Srivastava
Keyword(s):  
Starlike Functions ◽  
Higher Order ◽  
Positive Real Part ◽  
Bell Numbers ◽  
Positive Real ◽  
Sharp Bounds ◽  
Hankel Determinants ◽  
Coefficient Bounds ◽  
The Family ◽  
Schwarzian Derivatives

Abstract Let $\begin{array}{} \mathcal{S}^*_B \end{array}$ be the class of normalized starlike functions associated with a function related to the Bell numbers. By establishing bounds on some coefficient functionals for the family of functions with positive real part, we derive for functions in the class $\begin{array}{} \mathcal{S}^*_B \end{array}$ several sharp coefficient bounds on the first six coefficients and also further sharp bounds on the corresponding Hankel determinants. Bounds on the first three consecutive higher-order Schwarzian derivatives for functions in the class $\begin{array}{} \mathcal{S}^*_B \end{array}$ are investigated.

Coefficient inequalities for $q$-starlike functions associated with the Janowski functions

2019 ◽  
Vol 48 (2) ◽  
pp. 407-425 ◽  
Author(s):  
H. M. SRIVASTAVA ◽  
Bilal KHAN ◽  
Nazar KHAN ◽  
Qazi Zahoor AHMAD
Keyword(s):  
Starlike Functions ◽  
Janowski Functions ◽  
Coefficient Inequalities

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 A certain subclass of meromorphically q-starlike functions associated with the Janowski functions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shahid Mahmood ◽  
Qazi Zahoor Ahmad ◽  
H. M. Srivastava ◽  
Nazar Khan ◽  
Bilal Khan ◽  
...  
Keyword(s):  
Starlike Functions ◽  
Janowski Functions

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 A Study of Some Families of Multivalent q-Starlike Functions Involving Higher-Order q-Derivatives

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1470
Author(s):  
Bilal Khan ◽  
Zhi-Guo Liu ◽  
Hari M. Srivastava ◽  
Nazar Khan ◽  
Maslina Darus ◽  
...  
Keyword(s):  
Starlike Functions ◽  
Higher Order ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disk ◽  
Function Classes ◽  
The Family ◽  
Radius Problems ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In the present investigation, by using certain higher-order q-derivatives, the authors introduce and investigate several new subclasses of the family of multivalent q-starlike functions in the open unit disk. For each of these newly-defined function classes, several interesting properties and characteristics are systematically derived. These properties and characteristics include (for example) distortion theorems and radius problems. A number of coefficient inequalities and a sufficient condition for functions belonging to the subclasses studied here are also discussed. Relevant connections of the various results presented in this investigation with those in earlier works on this subject are also pointed out.

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