The Convergence Theorems Of Composite Implicit Iterative Process For Nonlinear Mappings

The convergence problems for nonlinear mapping is a very important research direction.In this paper,we discuss strong and weak convergence theorems of a new three step composite implicit iteration scheme for a finite family of asymptotically nonexpansive self-mappings and asymptotically nonexpansive nonself-mappings,and the strong convergence theorem for the composite iterative process for asymptotically hemi-pseudoco-ntractive mapping.The paper consists of four parts.The main contents of this paper are summarized as follows:The first chapter,we will introduce the background and the development of the topic at home and abroad,simply narrate the main content of the topic.The second chapter,we will discuss the strong convergence theorems of a new three step composite implicit iteration scheme for a finite family of asymptotically nonexpansive self-mappings and asymptotically nonexpansive nonself-mappings.The third chapter,we will discuss the the weak convergence theorems of a new three step composite implicit iteration scheme for a finite family of asmptotically nonexpansive self-mappings and asymptotically nonexpansive nonself-mappings.The fourth chapter,we will discuss the strong convergence theorem for the composite iterative process for asymptotically hemi-pseudocontractive mapping.