On a method of estimating derivatives in complex differential equations

Abstract

By a recent method to estimate the derivatives |w^(k)(z_i)|, \ k>1, at certain a-points of a meromorphic function w(z) in terms of the Ahlfors-Shimizu characteristic and of |w^{'}(z_i)|, 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.