Researches On Iterative Approximation Of Fixed Points For Nonlinear Mappings

Fixed point theory and its applications is a very important research topic in nonlinear functional analysis. In this paper, we will discuss strong and weak convergence theorems for with mean errors of mixed type asymptotically nonexpansive mappings and strong convergence of implicit iteration process with errors for two finite families of asymptotically nonexpansive mappings in uniformly convex Banach spaces.The paper consists of four parts. The main contents of this paper are summarized as follows:The first chapter, we will simply talk about the current research progress about the topic at home and abroad and the main content of the topic.The second chapter, we will discuss strong convergence theorems for with mean errors of mixed type asymptotically nonexpansive mappings.The third chapter, we will discuss weak convergence theorems for with mean errors of mixed type asymptotically nonexpansive mappings.The fourth chapter, we will discuss strong convergence of implicit iteration process with errors for two finite families of asymptotically nonexpansive mappings.