Approximating common fixed points of asymptotically nonexpansive maps in uniformly convex Banach spaces
نویسندگان
چکیده
We introduce three-step iterative schemes with errors for two and three nonexpansive maps and establish weak and strong convergence theorems for these schemes. Mann-type and Ishikawa-type convergence results are included in the analysis of these new iteration schemes. The results presented in this paper substantially improve and extend the results due to Khan and Fukhar-ud-din (2005), Shahzad (2005), Takahashi and Tamura (1995), Tan and Xu (1993) and Senter and Dotson (1974).
منابع مشابه
Convergence results: A new type iteration scheme for two asymptotically nonexpansive mappings in uniformly convex Banach spaces
In this article, we introduce a new type iterative scheme for approximating common fixed points of two asymptotically nonexpansive mappings is defined, and weak and strong convergence theorem are proved for the new iterative scheme in a uniformly convex Banach space. The results obtained in this article represent an extension as well as refinement of previous known resu...
متن کاملNew iteration process for approximating fixed points in Banach spaces
The object of this paper is to present a new iteration process. We will show that our process is faster than the known recent iterative schemes. We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized nonexpansive mappings. We also present a numerical example for proving the rate of convergence of our res...
متن کاملCommon fixed points of a finite family of multivalued quasi-nonexpansive mappings in uniformly convex Banach spaces
In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.
متن کاملStrong Convergence of an Implicit Iteration Process for Two Asymptotically Nonexpansive Mappings in Banach Spaces
The purpose of this paper is to introduce an implicit iteration process for approximating common fixed points of two asymptotically nonexpansive mappings and to prove strong convergence theorems in uniformly convex Banach spaces.
متن کاملOn fixed points of fundamentally nonexpansive mappings in Banach spaces
We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...
متن کاملFixed points for total asymptotically nonexpansive mappings in a new version of bead space
The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computers & Mathematics with Applications
دوره 53 شماره
صفحات -
تاریخ انتشار 2007