UNIQUENESS THEOREM FOR GENERAL DIFFERENTIAL POLYNOMIALS (P(f))(k) AND (P(g))(k) SHARING A SMALL FUNCTION

Abstract

Consider meromorphic functions f; g; and ; where is a small function with respect to f and consider a polynomial P: By using techniques of Nevanlinna theory, we give suitable conditions on the number of zeros and the multiplicities of the zeros of P0 so as to be able to show that if differential polynomials of the form (P(f))(k) and (P(g))(k) share counting multiplicities, then f = g. In this paper, we will consider the k-th derivative instead of the first derivative of the meromorphic functions. Thus, our work generalizes the related results due to Kamal Boussaf, Alain Escassut and
Jacqueline Ojeda [2].