Some subordinating results for classes of functions defined by Sǎlǎgean type q derivative operator

Aouf, K Mohamed; Mostafa, O Adela

doi:10.2298/fil2007283a

Cited by 6 publications

(2 citation statements)

References 27 publications

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“…An example accompanies the proved results employing the technique used earlier by Attiya [38], Srivastava and Attiya [39], and Singh [40]. Some special cases of this operator are also obtained by Aouf and Mostafa [41] and Frasin [42].…”

Section: Introductionmentioning

confidence: 59%

Applications of q-Calculus Multiplier Operators and Subordination for the Study of Particular Analytic Function Subclasses

et al. 2023

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In this article, a new linear extended multiplier operator is defined utilizing the q-Choi–Saigo–Srivastava operator and the q-derivative. Two generalized subclasses of q—uniformly convex and starlike functions of order δ—are defined and studied using this new operator. Necessary conditions are derived for functions to belong in each of the two subclasses, and subordination theorems involving the Hadamard product of such particular functions are stated and proven. As applications of those findings using specific values for the parameters of the new subclasses, associated corollaries are provided. Additionally, examples are created to demonstrate the conclusions’ applicability in relation to the functions from the newly introduced subclasses.

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Section: Introductionmentioning

confidence: 59%

Applications of q-Calculus Multiplier Operators and Subordination for the Study of Particular Analytic Function Subclasses

et al. 2023

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“…Jackson [15] 푞 − derivative, 0 < 푞 < 1, was defined by Annby and Mansour and other researchers [16][17][18][19][20][21] :…”

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confidence: 99%

Untitled

2023

Math. Syst. Sci.

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In this paper, we define a new subclass of bi-univalent functions of complex order ∑ (휏, 휁; 휑) which is defined by subordination in the open unit disc D by using 훻 퐹(휗) operator. Furthermore, using the Faber polynomial expansions, we get upper bounds for the coefficients of function belonging to this class. It is known that the calculus without the notion of limits is called q-calculus which has influenced many scientific fields due to its important applications. The generalization of derivative in q-calculus that is q-derivative was defined and studied by Jackson. A function 퐹 ∈ 퐴 is said to be bi-univalent in D if both F and F −1 are univalent in D. The class consisting of bi-univalent functions is denoted by σ. The Faber polynomials play an important role in various areas of mathematical sciences, especially in geometric function theory. The purpose of our study is to obtain bounds for the general coefficients |푎 |(푛 ≥ 3) by using Faber polynomial expansion under certain conditions for analytic bi-univalent functions in subclass ∑ (휏, 휁; 휙) and also, we obtain improvements on the bounds for the first two coefficients |푎 | and |푎 | of functions in this subclass. In certain cases, our estimates improve some of those existing coefficient bounds.

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Subordination factor sequence results for starlike and convex classes defined by q-Cătaş operator

Aouf

Madian

2021

Afr. Mat.

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Some subordinating results for classes of functions defined by Sǎlǎgean type q derivative operator

Abstract: In this paper, we investigate several interesting some subordination results for classes of analytic functions defined by the S?l?gean type q-derivative operator.

Cited by 6 publications

References 27 publications

Applications of q-Calculus Multiplier Operators and Subordination for the Study of Particular Analytic Function Subclasses

Applications of q-Calculus Multiplier Operators and Subordination for the Study of Particular Analytic Function Subclasses

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Subordination factor sequence results for starlike and convex classes defined by q-Cătaş operator

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