On The Convergence For Asymptotically Nonexpansive Mappings

The theory of fixed point is a strong tool for researching nonlinear functional analysisand equations. The purpose of this paper is to study convergence theorems about the mixedtype iterative and strong convergence theorems for generalized I-asymptoticallyquasi-nonexpansive mapping in Banach spaces.The paper consists of four parts. The main results of this paper are summarized asfollowing：In the first chapter, we simply narrate the academic background and relevantdevelopment of the issue. And the main content is introduced.In the second chapter, some definitions, lemmas and related results used in thearticle are introduced in the preparation.In the third chapter, convergence theorems about the mixed type iterative sequenceare given in Banach spaces.In the fourth chapter, strong convergence theorems for generalized I-asymptoticallyquasi-nonexpansive mapping are given in Banach spaces.