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

AIMS Mathematics

Rabha W. Ibrahim¹  Dumitru Baleanu² 

[1] 1 Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam 2 Faculty of Mathematics & Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;3 Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey 4 Institute of Space Sciences, R76900 Magurele-Bucharest, Romania 5 Department of Medical Research, China Medical University, Taichung 40402, Taiwan;

关键词: analytic function;    subordination and superordination;    univalent function;    open unit disk;    algebraic differential equations;    majorization method;   

DOI  :  10.3934/math.2021049

来源: DOAJ

【 摘 要 】

In this paper, a type of complex algebraic differential equations (CADEs) is considered formulating by \[\alpha [\varphi(z) \varphi” (z) +(\varphi' (z))^2]+ a_m \varphi^m(z)+a_{m-1} \varphi^{m-1}(z)+...+ a_1 \varphi(z)+ a_0=0.\] 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 $e^z.$ 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.

【 授权许可】

Unknown