Comprehensive subclasses of multivalent functions with negative coefficients defined by using a q-difference operator

El-Qadeem, Alaa H.; Mamon, Mohamed A.

doi:10.1016/j.trmi.2018.04.002

Cited by 10 publications

(7 citation statements)

References 7 publications

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“…For extra investigation, we inform the investigators to give some results and consequences related to other categories of smooth functions for instant, one can use harmonic mappings, p-valent or meromorphic maps. Moreover, El-Qadeem and Mamon [11] can use (7) to generalize their classes by extend the operator into p-valent class of analytic functions or generalize works in [29][30][31][32][33][34][35][36].…”

Section: Discussionmentioning

confidence: 99%

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Geometric process solving a class of analytic functions using q-convolution differential operator

Ibrahim

2020

Journal of Taibah University for Science

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In current realization, our object is to use the convolution product in terms of the notion quantum calculus to deliver a propagated q-derivative factor taking a more generalized Sàlàgean formula. By joining both the new factor together with the Janowski formula, we designate a special category of analytic factors in domain of unit disk. Finally, we deliberate a set of significant inequalities involving these classes. As applications, we seek the q-differential translator to generalize a denomination of differential equations species Briot-Bouquet and formulate its upper analytic solution using the subordination idea. This application can be employed in information theory and thermo dynamical systems.

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Section: Discussionmentioning

confidence: 99%

“…Moreover, El-Qadeem and Mamon presented different classes of q-calculus of p-valent Sàlàgean differential operator. These classes modified some recent works [11].…”

Section: Introductionmentioning

confidence: 87%

Geometric process solving a class of analytic functions using q-convolution differential operator

Ibrahim

2020

Journal of Taibah University for Science

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“…The coefficient characterization makes several computations in T manageable which can be very messy and very difficult for the whole of A. For very recent works related to functions with negative coefficients, we refer to [8,10,14,23,30,37,43,46,47]. Motivated by the above cited works on functions with negative coefficients, in this paper, we study various characteristic properties of the function class T UM γ (g, b, k, α given by…”

Section: Functions With Negative Coefficientsmentioning

confidence: 99%

Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator

Malik¹,

Dar

Sharma³

2021

EJMS

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We use the concept of convolution to introduce and study the properties of a unified family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$, $(0\leq\gamma\leq1,\,k\geq0)$, consisting of uniformly $k$-starlike and $k$-convex functions of complex order $b\in\mathbb{C}\setminus\{0\}$ and type $\alpha\in[0,1)$. The family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$ is a generalization of several other families of analytic functions available in literature. Apart from discussing the coefficient bounds, sharp radii estimates, extreme points and the subordination theorem for this family, we settle down the Silverman's conjecture for integral means inequality. Moreover, invariance of this family under certain well-known integral operators is also established in this paper. Some previously known results are obtained as special cases.

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“…Numerous integral and derivative features were formulated by using the convolution concept; for example, the Sàlàgean derivative [6], Al-Oboudi derivative (generalization of the Sàlàgean derivative) [7], and the symmetric Sàlàgean derivative [8]. It is significant to notify that the procedure of convolution finds its uses in different research, analysis, and study of the geometric properties of regular functions (see [9][10][11]). Here, we aim to study some geometric properties of a new quantum symmetric conformable differential operator (Q-SCDO).…”

Section: Introductionmentioning

confidence: 99%

On subclasses of analytic functions based on a quantum symmetric conformable differential operator with application

2020

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Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators, integral operators, and classes of analytic functions, especially the classes that are generated by convolution product (Hadamard product). In this effort, we aim to introduce a quantum symmetric conformable differential operator (Q-SCDO). This operator generalized some well-know differential operators such as Sàlàgean differential operator. By employing the Q-SCDO, we present subclasses of analytic functions to study some of its geometric solutions of q-Painlevé differential equation (type III).

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Comprehensive subclasses of multivalent functions with negative coefficients defined by using a q-difference operator

Cited by 10 publications

References 7 publications

Geometric process solving a class of analytic functions using q-convolution differential operator

Geometric process solving a class of analytic functions using q-convolution differential operator

Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator

On subclasses of analytic functions based on a quantum symmetric conformable differential operator with application

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