Applications of higher-order &lt;i&gt;q&lt;/i&gt;-derivatives to the subclass of &lt;i&gt;q&lt;/i&gt;-starlike functions associated with the Janowski functions

Rehman, Muhammad Sabil Ur; Ahmad, Qazi Zahoor; Srivástava, H. M.; Khan, Nazar; Darus, Maslina; Khan, Bilal

doi:10.3934/math.2021067

Cited by 27 publications

(12 citation statements)

References 30 publications

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“…Inequality (22) will be true if This gives |z| n+2p < (p−α)q p (p+1)[p+n,q](1+B)(1+[p,q]µ+µq p [p+n,q]) m (n+p+α)([p,q](A−B)(p+1)−2p[p,q](1+A))…”

Section: A Set Of Main Resultsmentioning

confidence: 99%

“…Very recently, by using q-Deference operator, Srivastava et al [14] studied a certain subclass of analytic function with symmetric points. Several other authors (see, for example, [15][16][17][18][19][20][21][22]) have studied and generalized the classes of symmetric and other q-starlike functions from different viewpoints and perspectives. For some more recent investigation about q-calculus, we may refer the interested reader to [23,24].…”

Section: Introduction Definitions and Motivationmentioning

confidence: 99%

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Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions

Shi

Ahmad²,

Khan

et al. 2021

Symmetry

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By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic multivalent close-to-convex functions with the help of a q-differential operator. Furthermore, we investigate some useful properties such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity for this new subclass.

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“…Inequality (22) will be true if This gives |z| n+2p < (p−α)q p (p+1)[p+n,q](1+B)(1+[p,q]µ+µq p [p+n,q]) m (n+p+α)([p,q](A−B)(p+1)−2p[p,q](1+A))…”

Section: A Set Of Main Resultsmentioning

confidence: 99%

Section: Introduction Definitions and Motivationmentioning

confidence: 99%

Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions

Shi

Ahmad²,

Khan

et al. 2021

Symmetry

Self Cite

View full text Add to dashboard Cite

show abstract

“…More recently, Srivastava et al [11,12] first defined certain subclasses of q-starlike functions and then studied their various properties including for example some coefficient inequalities, inclusion properties, and a number of sufficient conditions. Moreover, the subclasses of q-starlike functions associated with the Janwoski or some other functions have been studied by the many authors (see, for example, [13][14][15][16][17][18][19][20]). For some more recent investigations based upon the q-calculus, we may refer the interested reader to the works in [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”

Section: Introduction Definitions and Motivationmentioning

confidence: 99%

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

Srivástava

Ahmad³

et al. 2021

Symmetry

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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.

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“…Furthermore, Srivastava et al published a series of articles in which they concentrated upon the class of q-starlike functions from many different aspects and viewpoints (see in [18][19][20][21][22]). For some more recent investigations about the q-calculus, we may refer the interested reader to the recent works [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Introduction Definitions and Motivationmentioning

confidence: 99%

A Class of k-Symmetric Harmonic Functions Involving a Certain q-Derivative Operator

Srivástava

Khan

et al. 2021

Mathematics

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In this paper, we introduce a new class of harmonic univalent functions with respect to k-symmetric points by using a newly-defined q-analog of the derivative operator for complex harmonic functions. For this harmonic univalent function class, we derive a sufficient condition, a representation theorem, and a distortion theorem. We also apply a generalized q-Bernardi–Libera–Livingston integral operator to examine the closure properties and coefficient bounds. Furthermore, we highlight some known consequences of our main results. In the concluding part of the article, we have finally reiterated the well-demonstrated fact that the results presented in this article can easily be rewritten as the so-called (p,q)-variations by making some straightforward simplifications, and it will be an inconsequential exercise, simply because the additional parameter p is obviously unnecessary.

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Applications of higher-order <i>q</i>-derivatives to the subclass of <i>q</i>-starlike functions associated with the Janowski functions

Cited by 27 publications

References 30 publications

Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions

Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions

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

A Class of k-Symmetric Harmonic Functions Involving a Certain q-Derivative Operator

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