On a method of estimating derivatives in complex differential equations

Abstract

By a recent method to estimate the derivatives $\left|w^{\left(k\right)}\right(z_i\left)\right|,$$k>1$, at certain $a$-points of a meromorphic function $w\left(z\right)$ in terms of the Ahlfors-Shimizu characteristic and of $\left|w^{\prime }\right(z_i\left)\right|$, we improve some classical results on the growth of meromorphic solutions of certain algebraic differential equations. Moreover, we offer similar results for equations involving inverse derivatives and derivatives of a power $w^t$ of a meromorphic function $w$.