Riemann-Hilbert Boundary -value Problems For (?)=f In Unit Circle

In this paper,the Riemann-Hilbert boundary -value problems of n-regular function in unit circle are discussed by the way of complex analy-sis.The Riemann-Hilbert boundary-value problems of anF/azn=f also are dis-cussed.In chapter one,the properties of n-regular function in unit circle and Dirichlet boundary-value problems are discussed. In the second chapter,the representation of n-regular functionΨ(z) in unit circle by analytic functionsφk(z)(k=0,1,…,n-1) in unit circle exclusively are investigated. The bound-ary conditions of n-regular fuctionΨ(z) are transformed into the boundary condition of analytic functionsφk(z)(k=0,1,…,n-1) in unit circle.The Riemann-Hilbert boundary-value problem of n-order nonhomogeneous equa-tion of anF/azn=f is suggested. It is concluded that the existence and represen-tations of solutions of n-order anF/azn=f in unit circle by Schwarz formula,The represtation of general solutions of n-order equations of nonhomogeneous by T-operator is also obtained.