Partial sums of generalized &lt;i&gt;q&lt;/i&gt;-Mittag-Leffler functions

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

doi:10.3934/math.2020028

Cited by 25 publications

(8 citation statements)

References 12 publications

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“…In this survey-cum-expository review article [13], the mathematical explanation and applications of the fractional q-calculus and the fractional q-derivative operators in geometric function theory were systematically investigated. For some more recent investigations about the recent usages of the q-calculus in geometric function theory, we may refer the interested readers to [14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Definition 5.…”

Section: Definitionmentioning

confidence: 99%

Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

et al. 2020

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First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization Rq(h) of the class R(h) of analytic functions, which are associated with the leaf-like domain in the open unit disk U, is given. Then, the coefficient estimates, the Fekete–Szegö problem, and the second-order Hankel determinant H2(1) for functions belonging to this class Rq(h) are investigated. Furthermore, similar results are examined and presented for the functions zf(z) and f−1(z). For the validity of our results, relevant connections with those in earlier works are also pointed out.

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Section: Definitionmentioning

confidence: 99%

Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

et al. 2020

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“…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]. Our present research is a continuation of some of these earlier developments.…”

Section: Introduction Definitions and Motivationmentioning

confidence: 86%

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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“…Additionally, the recently-published review article by Srivastava [9] is potentially useful for researchers and scholars working on these topics. For other recent investigations involving the q-calculus, one may refer to [17][18][19][20][21][22][23][24][25][26][27][28]. In this paper, we propose mainly to generalize the work presented in [29].…”

Section: A(1) := Amentioning

confidence: 99%

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

et al. 2020

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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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Partial sums of generalized <i>q</i>-Mittag-Leffler functions

Cited by 25 publications

References 12 publications

Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

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

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

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