On the characteristic functions of meromorphic functions sub-weighted sharing three values

Abstract

We say that two meromorphic functions f and g sub-weighted share a value a∈C‾ with level k if they have the same set of a-points counted with multiplicity for the value a, where all a-points with multiplicity exceeding k are omitted. In this paper, we investigate the relation between the characteristic functions of two meromorphic functions sub-weighted sharing three values. We show that if two non-constants meromorphic functions f and g share sub-weighted three distinct values a1,a2,a3 with level k1,k2,k3 respectively, then(1−ϵ−δϵ)T(r,f)≤(2+ϵ+δϵ)T(r,g)+S(r,g) for every positive number ϵ, where δϵ=(24ϵ2+16ϵ4)(1k1+1+1k2+1+1k3+1). Our result is the extension of the previous result of P. Li and C. C. Yan [7] and others.