Coefficient Inequalities for Multivalent Janowski Type q-Starlike Functions Involving Certain Conic Domains

Rehman, Muhammad Sabil Ur; Ahmad, Qazi Zahoor; Al-Shbeil, Isra; Ahmad, Shamim; Khan, Ajmal; Khan, Bilal; Gong, Jianhua

doi:10.3390/axioms11100494

Cited by 10 publications

(6 citation statements)

References 24 publications

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“…Ultimately, this investigation is a contribution to knowledge, through the introduction of a new integral operator, exploring its applications in GFT, and providing insights into the geometric properties of the new class of analytic functions. For some related examples, see [45,46,[50][51][52][53].…”

Section: Discussionmentioning

confidence: 99%

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Concerning a Novel Integral Operator and a Specific Category of Starlike Functions

Lasode,

Opoola,

Al-Shbeil

et al. 2023

Mathematics

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In this study, a novel integral operator that extends the functionality of some existing integral operators is presented. Specifically, the integral operator acts as the inverse operator to the widely recognized Opoola differential operator. By making use of the integral operator, a certain subclass of analytic univalent functions defined in the unit disk is proposed and investigated. This new class encompasses some familiar subclasses, like the class of starlike and the class of convex functions, while some new ones are introduced. The investigation thereafter covers coefficient inequality, distortion, growth, covering, integral preserving, closure, subordinating factor sequence, and integral means properties. Furthermore, the radii problems associated with this class are successfully addressed. Additionally, a few remarks are provided, to show that the novel integral operator and the new class generalize some existing ones.

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Section: Discussionmentioning

confidence: 99%

“…, the class studied by Altintaş [40] for functions f ∈ A whose coefficients are negative. The aforementioned subclasses and those in [20,21,23,25,31,45,46] are some of the motivations for the choice of the new class G n j (b, t, u, β, δ).…”

mentioning

confidence: 99%

Concerning a Novel Integral Operator and a Specific Category of Starlike Functions

Lasode,

Opoola,

Al-Shbeil

et al. 2023

Mathematics

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“…In addition, we proved that these results are sharp, and, for the special values of the parameters, we determined certain consequences of our main results. More information related to this work can be found at [33][34][35][36][37].…”

Section: Discussionmentioning

confidence: 99%

Sharp Estimates Involving a Generalized Symmetric Sălăgean q-Differential Operator for Harmonic Functions via Quantum Calculus

Al-Shbeil,

Khan,

Tchier

et al. 2023

Symmetry

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In this study, we apply q-symmetric calculus operator theory and investigate a generalized symmetric Sălăgean q-differential operator for harmonic functions in an open unit disk. We consider a newly defined operator and establish new subclasses of harmonic functions in complex order. We determine the sharp results, such as the sufficient necessary coefficient bounds, the extreme of closed convex hulls, and the distortion theorems for a new family of harmonic functions. Further, we illustrate how we connect the findings of previous studies and the results of this article.

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“…In their paper [6], Arif et al defined and explored the q-derivative operator for multivalent functions, and [7] Zang et al defined a generalized conic domain and then investigated a novel subclass of q-starlike functions using the definition of subordination and q-calculus operator theory. Recently, many well-known mathematicians have used q-calculus and studied some subclasses of analytic functions and their properties (see, for example, [8,9]). Recently, several authors published a series of studies [10][11][12] focusing on the classes of q-starlike functions connected to Janowski functions [13] from various angles.…”

Section: Introduction and Definitionsmentioning

confidence: 99%

The Properties of Meromorphic Multivalent q-Starlike Functions in the Janowski Domain

Al-Shbeil

Gong

Ray³

et al. 2023

Fractal Fract

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Many researchers have defined the q-analogous of differential and integral operators for analytic functions using the concept of quantum calculus in the geometric function theory. In this study, we conduct a comprehensive investigation to identify the uses of the Sălăgean q-differential operator for meromorphic multivalent functions. Many features of functions that belong to geometrically defined classes have been extensively studied using differential operators based on q-calculus operator theory. In this research, we extended the idea of the q-analogous of the Sălăgean differential operator for meromorphic multivalent functions using the fundamental ideas of q-calculus. With the help of this operator, we extend the family of Janowski functions by adding two new subclasses of meromorphic q-starlike and meromorphic multivalent q-starlike functions. We discover significant findings for these new classes, including the radius of starlikeness, partial sums, distortion theorems, and coefficient estimates.

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Coefficient Inequalities for Multivalent Janowski Type q-Starlike Functions Involving Certain Conic Domains

Cited by 10 publications

References 24 publications

Concerning a Novel Integral Operator and a Specific Category of Starlike Functions

Concerning a Novel Integral Operator and a Specific Category of Starlike Functions

Sharp Estimates Involving a Generalized Symmetric Sălăgean q-Differential Operator for Harmonic Functions via Quantum Calculus

The Properties of Meromorphic Multivalent q-Starlike Functions in the Janowski Domain

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