Properties Of Some Functions Related To Ruscheweyh Derivative

Since S.Ruscheweyh[26]defined the Ruscheweyh derivative of the analytic function,many scholars have studied univalent or multi-valent analytic functions related to Ruscheweyh derivative.In 1975,S.Ruscheweyh gave some new criteria for univalent functions.then in 1997,S.Kanas and H.M.Srivastava[13]combined S.Ruscheweyh's results,expounding criterion of univalent function.In 2015,E.Deniz and H.Orhan[4]let A denote the class of analytic functions,and studied univalence criteria related with Ruscheweyh derivative,as the same time obtained some sufficient conditions for the univalence.Also they know the new and simpler conditions for the integral operator in paper.In 2016,H.M.Srivastava,P.Sharma and R.K.Raina[30]defined the class of analytic functions Am and some new function class,such as S?v,n(?,?),C?v,n(?,?,?)and so on and then prove several inclusion results for each of these classes of analytic functions.The results generalize the conclusions obtained by S.Owa,S.Ruscheweyh and so on.Motivated by their work,we define class of Meromorphic function ?m and p-valent analytic function Ap,combing Ruscheweyh derivative in the third part of this article,we discuss some inclusion relation and univalence criteria in this paper.The paper consists of three parts.The main contents of each part are as follows:The first part is introduction and preliminary results.It introduces the basic concepts?three lemmas and some classes of function involved in the paper.The second part is inclusion relation of function class.Using lemma 1 and lemma 2 prove the inclusion relation of A?v,n(?,?),B?v,n(?,?m?)and E?v,n(?,?,?,?).The third part is univalence criteria.Using lemma 3 try to obtain some sufficient conditions for the operator F?(z)in the paper.