Approximation Of Fixed Points Of Non-self Asymptotically Nonexpansive Mappings

The fixed point theory is an important part of nonlinear functional analysis. In re-cent years, the study of asymptotically nonexpansive mappings have become more andmore, but the two definition of non-self asymptotically nonexpansive mappings and afinite of non-self asymptotically nonexpansive mappings haven't been study more. Inthis paper, as C. E. Chidume,H.Y. Zhou,Xiang changhe, we study the two definitionof non-self asymptotically nonexpansive mappings and a finite of non-selfasymptotically nonexpansive mappings.In this paper, we discuss and know the relationship of the two definition ofnon-self asymptotically nonexpansive mappings. Then in uniformly convex Banachspace satisfying Opial's condition, we study a finite of the first and second kind of thenon-self asymptotically nonexpansive mappings about N-step iterative algorithm.This paper includes four chapters．In chapter1,we discuss the significance ofthis paper. We present some research situation about non-self asymptotically nonexpansivemappings.In chapter2,we discuss the two definition of non-self asymptotically nonexpansivemappings and know the relationship of them. We give the example of the second mappingsand show it more extensive.In chapter3, in uniformly convex Banach space satisfying Opial's condition, westudy the convergence about N-step iterative algorithm of a finite of the first kind of thenon-self asymptotically nonexpansive mappingsIn chapter4, in uniformly convex Banach space satisfying Opial's condition, we study theconvergence about iterative algorithm of a finite of the second kind of the non-self asymptotically nonexpansive mappings.