The Sufficient And Necessary Conditions For The Strong Convergence Of Asymptotically Hemi-pseudocontractive Mapping

One of the mainly focused problems of fixed point theory is iterative approximation isdiscussed in this paper. The strong convergence of the asymptoticallyhemi-pseudoncontractive mapping and the weak convergence of the asymptoticallynonexpansive nonself-mapping for the different iterative sequence are discussed in Banachspace.The paper consists of four parts. The main contents of this paper are summarized asfollows：The first chapter, we will simply narrate the background and discuss the develop-ment of iterative sequence.The second chapter, we will discuss the sufficient and necessary conditions for theasymptotically hemi-pseudocontractive for the modified Ishikawa iterative with errors.The third chapter, we will discuss the sufficient and necessary conditions for theasymptotically hemi-pseudocontractive for the three-step iterative.The fourth chapter, weak convergence theorems for asymptotically nonexpansivenonself-mappings are obtained in Banach space.