The Problem Of The Radius Of Starlikeness Of Partical Sums Of Analytic Functions

Content: In this thesis, we investigate the problem of the radius of starlikeness of partical sums of univalent functions and the problem of the radius of starlikeness of partical sums of analytic functions。 In chapter 1, we introduce some preparating definitions。 In chapter 2, for the functionsand when k = 6, we prove that all the S_6,n (z) will be starlike functions in the domain |z|<(3/7)^1/6, and the best radius is |z|<(3/7)^1/6。 In chapter 3, we investigate the radius of starlikeness of partical sum of analytic functions。 For the functionand when c = 2 , we prove that all the S_n(z,g) are starlike functions in |z|<(3/16) ,and the best radius is (3/16)。 In chapter 4, we investigate the radius of starlikeness ofintegral operator , we prove that when f∈S*(α)that F(z)∈S*(α) and we obtain the sufficient condition for F(z)∈S*(α) byusing differential subordination 。 In chapter 5, we give the application of the radius of starlikeness。 We prove that Ruscheweyh's Multiplier conjecture is true in some special conditions by using the radius of starlikeness of partical sums of univalent functions。...