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

In this paper, a type of complex algebraic differential equations (CADEs) is considered formulating by alpha[phi(z)phi ''(z) + (phi'(z))(2)] + a(m)phi(m)(z) + a(m-1)phi(m-1)(z) + ... + a(1)phi(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.