PROPERTIES FOR TWO CLASSES OF p-VALENTLY MEROMORPHIC FUNCTIONS

The definition of differential operator Ikp is first given,and then two classes of p-valently meromorphic functions ∑(S)*p-1(k,α,β) and ∑(C)p-1(k,α,β) by means of the operator Ikp are introduced.The coefficient inequalities of this two classes of functions are obtained by applying the analytical method and technique,and the function class ∑Ghψ(Cn+p) is also introduced.Next by making use of coefficient characterizations of function classes ∑(S)*p-1(k,α,β) and ∑(C)p-1(k,α,β),the main conclusions of this paper are derived.That is,the Hadamard product of functions which combined with finite functions in ∑(S)*p-1(k,α,β) and finite functions in ∑(C)p-1(k,α,β) belongs to the class ∑Ghψ(Cn+p).Furthermore,the distortion theorems and integral transforms related to this two classes are provided.