The deficient values of a class of meromorphic functions

Abstract

In this paper, we study the deficient -values and the Nevanlinna deficiencies of meromorphic functions f(z) of the form f(z) -P(g(z)), where P(z) is a polynomial and g{z) is a meromorphic function with two Picard exceptional values. In fact, we prove that all deficient values of f(z) are of the form P(a), where o is a Picard exceptional value of g(z). Furthermore, if g(z) is of finite order, we compute explicitly the Nevanlinna deficiencies for f(z). We also give an upper bound estimation for the deficiencies of f(z) while g(z) is of infinite order.