| In recent years,Iterative techniques for approximating fixed points of nonexpansire mappings or asymptotically nonexpansive(type) mappings have been studied by a number of authors,using the Mann iteration process or the Ishikawa iteration process.As a matter of fact,several new iterative schemes are introduced and studied in this paper.This paper will discuss it in the following way:In section 1,the purpose is to prove a novel inequality on sequence and some sufficient and necessary conditions on the strong convergence of a new iterative process for nonexpansive mappings in convex metric spaces.In section 2,it is proved a new inequality on sequence and some sufficient and necessary conditions for a new iterative scheme converges to the fixed point of the asymptotically quasi-nonexpanswe mappings.In section 3,a new iterative scheme,viewed as an extension for Ishikawa iteration with errors,is introduced and studied for nonself generalized asymptotically quasi-nonexpansive mappings in Banach spaces.It is remarked that the results presented in this paper are new even for nonexpansive maps.Thus,our results generalize and unify the corresponding results. |
