Meromorphic functions that weighted sharing three values and one pair

Abstract

G. Brosch improved the theorem of Nevanlinna for four values theorem and proved that let f and g be two nonconstant meromorphic functions sharing 0, 1, ∞ CM, and let a and b be two finite complex numbers such that a, b $\ otin$ {0, 1}. If f = a ⇔ g = b, then f is a fractional linear transformation of g. In this paper we extend this theorem by using the idea of weighted sharing.