Some Related To Linear Operator More Meromorphic Function

Geometric function theory mainly investigates geometrical properties of analytic function, it is a mathematical field and has attracted great attention of many mathematicians. Geometry is related to analysis. Univalent functions and subordinate principle are the important contents of geometric function theory which include the theoretical study of growth theorem、area theorem、distortion theorem、coefficient estimation、subordinate principle and differential subordination,etc.Since the1970s and1980s,with the application of convolution theory and differential subordination, many mathematicians based on analytic functions and applied convolution n hyper-geometric functions to creat many operators,and did some useful research jobs,such as Liu and Patel[9]、Srivastava[7]、 Cho[5]、Kwon and Srivastava [4]. In recent years, many scholars have focused on the properties of the analytic functions with negative coeffcients, and they have constructed a lot of operators by using convolution theory and differential subordination. After Patel[9] gave multi-valent analytic functions of generalized fractional differential integral operator Ωz(λ,ρ), Liu and Patel used the operators to constructe the functionFα (z),and studied the subordination relations between Fα(j)(z)and(Ωz(λ,ρ)f(z))(j) After that, Liu and srivastava[11], Raina and srivastava [7]did hard work on the operator Hpq,s (5,),they used the operator Hpq,s (9,) to create subclasses of the analytic functions,and studied the coefficient estimation、differential subordination、inclusion relations、 integral representations and convolution properties of these functions.Motivated by their work, in the present paper,we introduce and investigate each of the following new subclasses Fp,kλ (a;a,c;h)、Mρλ(a;a,c;h)and Qρλ (a;a,c;h), which are defined by convolution theory and differential subordination.Such results as inclusion relations s integral representations and convolution properties for these function classes are proved.The results presented here provide extensions of those given in some earlier works.There are five parts in this article.The first part is introduction: We introduce p-valent meromorphic functions, differential subordination, Hadamard convolution and class Fp,kλ (a;a,c;h)、Mρλ(a;a,c;h) andQpλ(a;a,c;h).The second part is lemma: do some preparations for the third and the fourth part.The third part are some inclusion relationships: this is one of the main conclusions of this paper. This part mainly discusses inclusion relationships of class Fp,kλ(a; a, c; h), Mpλ(a; a, c; h) and Qpλ(a;a,c;h).The fourth part mainly discuss convolution and integral representation of class Fp,kλ(a;a,c;h), Mpλ(a;a,c;h) and Qpλ(a;a,c;h), meanwhile investigate some related properties of the operator Lm(f).