An Improved Inequality for Meromorphic Functions with Few Simple Zeros

Abstract

Suppose that f(z) is a non-constant meromorphic function in the complex plane satisfying N_(1))(r,f)=S(r,f) and d is a non-zero constant.Then the author proves thatT(r,f)11N(r,f)+11N(r,f′+df-1)+S(r,f),except that f(z) is one of the following forms:(i) Ae~(-dz);(ii) d(Ae~(-dz)+1)~2;(iii) d(Ae~(-2z)-1)~2;(iv) Ae~(dz)(e~(-dz)+2dA)~2,where A is a non-zero constant.