Third order differential super ordination and sub-ordination results for multivalent meromorphically functions associated with Wright function

Taha, Abdul Kader Yasin; Juma, Abdul Rahman S.

doi:10.1063/5.0134582

Cited by 3 publications

(3 citation statements)

References 6 publications

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“…They extended the theory of second-order differential subordination in U introduced by Miller and Mocanu [10] to the third-order case that satisfy the third-order differential subordination {ψ(p(z), zp (z), z 2 p (z), z 3 p (z); z) : z ∈ U } ⊂ Ω. Recently, the several authors have considered the applications of these results to third-order differential subordination for analytic functions in U for example (see [1,3,4,7,8,13,[15][16][17]). In 2020, Atshan et al [2] extended the theory of third-order differential subordination in U introduced by Antonino and Miller [1] to the fourth-order case.…”

Section: Definitions and Main Resultsmentioning

confidence: 99%

$K^{th}$-order Differential Subordination Results of Analytic Functions in the Complex Plane

Wanas,

Soren

2024

EJMS

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In recent years, there have been many interesting usages for differential subordinations of analytic functions in Geometric Function Theory of Complex Analysis. The concept of the first and second-order differential subordination have been pioneered by Miller and Mocanu. In 2011, the third-order differential subordination were defined to give a new generalization to the concept of differential subordination. While the fourth-order differential subordination has been introduced in 2020. In the present article, we introduce new concept that is the Kth-order differential subordination of analytic functions in the open unit disk U.

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Section: Definitions and Main Resultsmentioning

confidence: 99%

$K^{th}$-order Differential Subordination Results of Analytic Functions in the Complex Plane

Wanas,

Soren

2024

EJMS

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“…Additionally, corresponding third-order differential superordinations can be explored employing the dual theory of third-order differential superordination, potentially connecting the findings of such a study with current findings through sandwich-type theorems as it can be seen in recent investigations like [31,32].…”

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confidence: 87%

New Applications of Gaussian Hypergeometric Function for Developments on Third-Order Differential Subordinations

Oros

Preluca

2023

Symmetry

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The main objective of this paper is to present classical second-order differential subordination knowledge extended in this study to include new results regarding third-order differential subordinations. The focus of this study is on the main problems examined by differential subordination theory. Hence, the new results obtained here reveal techniques for identifying dominants and the best dominant of certain third-order differential subordinations. Another aspect of novelty is the new application of the Gaussian hypergeometric function. Novel third-order differential subordination results are obtained using the best dominant provided by the theorems and the operator previously defined as Gaussian hypergeometric function’s fractional integral. The research investigation is concluded by giving an example of how the results can be implemented.

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“…The two dual theories of third-order differential subordination and superordination continue to develop nicely. Very recent results obtained using this approach can be found in papers like [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

New Developments on the Theory of Third-Order Differential Superordination Involving Gaussian Hypergeometric Function

Oros,

Preluca

2023

Mathematics

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The present research aims to present new results regarding the fundamental problem of providing sufficient conditions for finding the best subordinant of a third-order differential superordination. A theorem revealing such conditions is first proved in a general context. As another aspect of novelty, the best subordinant is determined using the results of the first theorem for a third-order differential superordination involving the Gaussian hypergeometric function. Next, by applying the results obtained in the first proved theorem, the focus is shifted to proving the conditions for knowing the best subordinant of a particular third-order differential superordination. Such conditions are determined involving the properties of the subordination chains. This study is completed by providing means for determining the best subordinant for a particular third-order differential superordination involving convex functions. In a corollary, the conditions obtained are adapted to the special case when the convex functions involved have a more simple form.

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Third order differential super ordination and sub-ordination results for multivalent meromorphically functions associated with Wright function

Cited by 3 publications

References 6 publications

$K^{th}$-order Differential Subordination Results of Analytic Functions in the Complex Plane

$K^{th}$-order Differential Subordination Results of Analytic Functions in the Complex Plane

New Applications of Gaussian Hypergeometric Function for Developments on Third-Order Differential Subordinations

New Developments on the Theory of Third-Order Differential Superordination Involving Gaussian Hypergeometric Function

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