Convex Subordination Chain And Bounded Construction Of Complex λ-order Almost Starlike Mappings

In this master’s thesis,the author mainly discusses some properties of convex subordination chain on the ellipsoid Qm={(Z1,Z2):|Z1|2+|Z2|m＜1}(m≥2),and f(z,t)is a convex dependent subordination chain under different conditions.Some analytical features of complex A-order almost starlike mappings on B2 are also discussed.At the same time,it is proved by the method of Loewner chain under certain conditions,maintain starlike characterThis article is divided into three chaptersIn the first chapter,we briefly introduced the background of the development of the geometric function theory of multiple complex variables.Some preliminary knowledge and main results used in this paper are describedIn Chapter 2,we generalize some results of the convex subordination chain on the n-dimensional unit sphere to the ellipsoid Ωm,and verify that f(z,t)is a necessary and sufficient condition for the convex subordination chain.In addition,the results of the subordination chain and its convex subordination chain on the unit disk D,and n-dimensional unit sphere are used to refine the application of the convex subordination chain on the ellipsoid QmIn Chapter 3,we study some properties of the complex A-order almost starlike mappings on B2 and prove the equivalent characterization of polynomial almost starlike mappings under different conditions.On the other hand,we also study the properties of Loewner chain angles to characterize the complex A-order almost starlike mappings on B2,and verify that f is a complex A-order almost starlike mappings on B2 that are equivalent to each otherThe main result of this article is the extension and improvement of related results on the premise of existing conclusions.In particular,embedding Loewner chain can solve many problems and can easily construct many holomorphic mappings.Drawing on relevant knowledge,the same method is used to verify some theorems to make the existing results more beautiful.