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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Keywords
Algebraic Differential Equations, Analytic Function, Majorization Method, Open Unit Disk, Subordination and Superordination, Univalent Function
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Citation
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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Source
AIMS Mathematics
Volume
6
Issue
1
Start Page
806
End Page
820