Fixed points for total asymptotically nonexpansive mappings in a new version of bead ‎space‎

نویسنده

  • A. Razani Department of Mathematics, Collage of ‎Science, Takestan Branch, Islamic Azad University, Takestan, Iran.‎
چکیده مقاله:

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, we define a new version of bead space and called it $CN$-bead space. Then the existence of fixed point for asymptotically nonexpansive mapping and total asymptotically nonexpansive mapping in $CN$-bead space are proved. In other word, Let $K$ be a bounded subset of complete $CN$-bead space $X$. Then the fixed point set $F(T)$, where $T$ is a total asymptotically nonexpansive selfmap on $K$, is nonempty and closed. Moreover, the fixed point set $F(T)$, where $T$ is an asymptotically nonexpansive selfmap on $K$, is ‎nonempty.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

fixed 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 کامل

Approximating Fixed Points of Total Asymptotically Nonexpansive Mappings

The class of asymptotically nonexpansive maps was introduced by Goebel and Kirk [18] as a generalization of the class of nonexpansive maps. They proved that if K is a nonempty closed convex bounded subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self-mapping of K , then T has a fixed point. Alber and Guerre-Delabriere have studied in [3–5] weakly contracti...

متن کامل

common fixed points of jointly asymptotically nonexpansive mappings

a definition of two jointly asymptotically nonexpansive mappings s and t on uniformly convex banach space e is studied to approximate common fixed points of two such mappings through weak and strong convergence of an ishikawa type iteration scheme generated by s and t on a bounded closed and convex subset of e. as a consequence of the notion of two jointly asymptotically nonexpansive maps, we c...

متن کامل

Fixed Points of Asymptotically Regular Nonexpansive Mappings on Nonconvex Sets

It is shown that if X is a Banach space and C is a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets {Ci : 1≤ i≤ n} of X , and each Ci has the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self-mapping of C has a fixed point. We also generalize the Goebel-Schöneberg theorem to some Banach...

متن کامل

Viscosity Approximation Methods for Fixed Points of Asymptotically Nonexpansive Mappings in Banach Space

In this paper, under the framework of Banach space with uniformly Gateaux differentiable norm and uniform normal structure, we use the existence theorem of fixed points of Li and Sims to investigate the convergence of the implicit iteration process and the explicit iteration process for asymptotically nonexpansive mappings. We get the convergence theorems.

متن کامل

A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings

Let E be a real Banach space, and K a closed convex nonempty subset of E. Let T1, T2, . . . , Tm : K → K bem total asymptotically nonexpansive mappings. A simple iterative sequence {xn}n≥1 is constructed inE and necessary and sufficient conditions for this sequence to converge to a common fixed point of {Ti}i 1 are given. Furthermore, in the case that E is a uniformly convex real Banach space, ...

متن کامل

منابع من

با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ذخیره در منابع من قبلا به منابع من ذحیره شده

{@ msg_add @}


عنوان ژورنال

دوره 6  شماره 4

صفحات  329- 332

تاریخ انتشار 2014-12-01

با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023