Certain family of integral operators associated with multivalent functions preserving subordination and superordination

Aouf, M. K.; Mostafa, A. O.; Zayed, H. M.

doi:10.2298/fil1807395a

Cited by 2 publications

(1 citation statement)

References 15 publications

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“…We should pay special attention to the fact that in Miller and Mocanu, 20 the sharp subordination (i.e., the best dominants for some subordinations) is the univalent solution of some differential equations. For a detailed historical survey and an extended list of references on differential subordinations and their applications to the theory of univalent and multivalent functions, we refer, for example, to other studies [28][29][30][31][32][33][34][35][36][37][38][39] and elsewhere. Finally, we note that differential equations have a practical interest in real-world applications such as COVID-19, cancer modeling, and fluid flows problems.…”

Section: Introductionmentioning

confidence: 99%

Third‐order differential subordinations for multivalent functions in the theory of source‐sink dynamics

Morais

Zayed

Srivastava

2021

Math Methods in App Sciences

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We propose third‐order differential subordination results associated with new admissible classes of multivalent functions defined in the open unit disk on the complex plane. Besides, we investigate the geometric properties of multivalent functions associated with a novel convolution operator. This is done by taking suitable linear combinations of the classical Gaussian hypergeometric function and its derivatives up to third‐order and applying the Hadamard product (or convolution) formula for power series. The complex velocity potential and the stream function of two‐dimensional potential flow problems over a circular cylinder using both sources with sink and two sources are treated by the methods developed in the present paper. We further determine the fluid flow produced by a single source and construct a univalent function so that the image of source/sink is also source/sink for a given complex potential. Finally, some plot simulations are provided to illustrate the different results of this work.

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Section: Introductionmentioning

confidence: 99%

Third‐order differential subordinations for multivalent functions in the theory of source‐sink dynamics

Morais

Zayed

Srivastava

2021

Math Methods in App Sciences

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Certain differential subordination results for univalent functions associated with $ q $-Salagean operators

Amini

Fardi

Al‐Omari

et al. 2023

MATH

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<abstract><p>In this paper, we employ the concept of the $ q $-derivative to derive certain differential and integral operators, $ D_{q, \lambda}^{n} $ and $ I_{q, \lambda}^{n} $, resp., to generalize the class of Salagean operators over the set of univalent functions. By means of the new operators, we establish the subclasses $ M^n_{q, \lambda} $ and $ D^n_{q, \lambda} $ of analytic functions on an open unit disc. Further, we study coefficient inequalities for each function in the given classes. Over and above, we derive some properties and characteristics of the set of differential subordinations by following specific techniques. In addition, we study the general properties of $ D_{q, \lambda}^{n} $ and $ I_{q, \lambda}^{n} $ and obtain some interesting differential subordination results. Several results are also derived in some details.</p></abstract>

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Certain family of integral operators associated with multivalent functions preserving subordination and superordination

Cited by 2 publications

References 15 publications

Third‐order differential subordinations for multivalent functions in the theory of source‐sink dynamics

Third‐order differential subordinations for multivalent functions in the theory of source‐sink dynamics

Certain differential subordination results for univalent functions associated with $ q $-Salagean operators

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