On differential polynomials, fixpoints and critical values of meromorphic functions

We prove some results concerning functions ƒ meromorphic of finite lower order in the plane, such that ƒƒ″−α(ƒ′)2 has few zeros, where α is a constant, using in part new estimates for the multipliers at fixpoints of certain functions. We go on to consider zeros of derivatives and the minimal lower growth of meromorphic functions with finitely many critical values. © 1999, Birkhäuser Verlag, Basel.