Iterative Algorithms For The Fixed Points Of Several Kinds Of Asymptotically Quasi-pseudo-contractive-type Mappings

The main of this paper is to investigate the strong convergence problems of a modi-fied Ishikawa iterative sequence with errors for asymptotically quasi-pseudo-contractive-type mappings, the viscosity approximating method of a common zero for a finite fam-ily of accretive operators and a new iterative algorithm for the fixed points of an asymp-totically nonexpansive mapping.The first result is that we introduce a modified Ishikawa iterative sequence with errors{xn} in an arbitrary real Banach space We also prove that the iterative sequence{xn} converges strongly to a fixed point of an asymototically nonexpansive mapping in the intermediate sense and an asymptotically quasi-pseudo-contractive-type mapping.In the strictly convex and reflexive Banach space which has a weakly continuous duality mapping J(?) with gauge (?), the second result is that we introduce a new viscosity approximating sequence{xn} useing the resolvent of accretive operators Under certain conditions, we prove the sequence{xn} converges strongly to a common zero of a finite family for accretive mappings.The third result is that we introduce a new iterative algorithm{xn} for the fixed points of an asymptotically nonexpansive mapping in an uniformly convex Banach space defined byUnder certain conditions, we prove the sequence{xn} converges strongly to a fixed point of the asymptotically nonexpansive mapping, the fixed point is also a solution of the following variational inequalityThe results here extend and improve the corresponding results reported by some other authors recently.The structure is that:we introduce some related research backgrounds, some rele-vant concepts and lemmas in the first chapter; in the second chapter, we prove the strong convergence problem of a modified Ishikawa iterative sequence with errors; in the third chapter, we study the viscosity approximating method of a common zero for a finite family of accretive operators; in the fourth chapter, we discuss on a iterative algorithm for the fixed points of an asymptotically nonexpansive mapping.