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Geometric behavior of a class of algebraic differential equations in a complex domain using a majorization concept

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Date

2020

Authors

Ibrahim, Rabha W.
Baleanu, Dumitru

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Abstract

In this paper, a type of complex algebraic differential equations (CADEs) is considered formulating by α[ϕ(z)ϕ′′(z) + (ϕ′(z))2] + amϕm(z) + am−1ϕm−1(z) + … + a1ϕ(z) + a0 = 0. The conformal analysis (angle-preserving) of the CADEs is investigated. We present sufficient conditions to obtain analytic solutions of the CADEs. We show that these solutions are subordinated to analytic convex functions in terms of ez. Moreover, we investigate the connection estimates (coefficient bounds) of CADEs by employing the majorization method. We achieve that the coefficients bound are optimized by Bernoulli numbers. © 2021 the Author(s), licensee AIMS Press.

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Algebraic Differential Equations, Analytic Function, Majorization Method, Open Unit Disk, Subordination and Superordination, Univalent Function

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Ibrahim, Rabha W.; Baleanu, Dumitru (2020). "Geometric behavior of a class of algebraic differential equations in a complex domain using a majorization concept", AIMS Mathematics, Vol. 6, No. 1, pp. 806-820.

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AIMS Mathematics

Volume

6

Issue

1

Start Page

806

End Page

820