BOUNDS FOR THE DERIVATIVE OF CERTAIN MEROMORPHIC FUNCTIONS AND ON MEROMORPHIC BLOCH-TYPE FUNCTIONS

It is known that if f is holomorphic in the open unit disc D of the complex plane and if, for some c > 0, vertical bar f (z)vertical bar <= 1/(1-vertical bar z vertical bar(2))(c), z is an element of D, then vertical bar f '(z)vertical bar <= 2(c + 1)/(1-vertical bar z vertical bar(2))(c+1). We consider a meromorphic analogue of this result. Furthermore, we introduce and study the class of meromorphic Bloch-type functions that possess a nonzero simple pole in D. In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class.